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Recent questions tagged random-variable
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121
Probability - Gravner-66
You are dealt one card at random form a full deck and your opponent is dealt $2$ cards (Without any replacement ). If you get an Ace, he pays you $10$ dollar, if you get a King, he pays you $5$ dollar (regardless of his cards). If you have ... red cards, he pays you $1$ dollar. In all other cases you pay him $1$ dollar . Determine your expected earnings . Are they positive?
Pooja Khatri
asked
in
Probability
Sep 25, 2018
by
Pooja Khatri
351
views
probability
gravner
engineering-mathematics
random-variable
0
votes
0
answers
122
Probability - Gravner-65.d
A biologist needs at least $3$ mature specimens of certain plant. The plant needs a year to reach maturity; once a seed is planted, any plant will survive for the year with probability $1/1000$ (independently of other plants). The biologist plants $3000$ ... the biologist should plant in order to get at least $3$ mature plants in a year with probability at least $0.999$.
Pooja Khatri
asked
in
Probability
Sep 25, 2018
by
Pooja Khatri
314
views
gravner
probability
engineering-mathematics
random-variable
0
votes
0
answers
123
Probability - Gravner-65.b
A biologist needs at least $3$ mature specimens of certain plant. The plant needs a year to reach maturity; once a seed is planted, any plant will survive for the year with probability $1/1000$ (independently of other plants). The ... these seeds reach maturity. (b) Write down a relevant approximate expression for the probability from(a).Justify briefly the approximation.
Pooja Khatri
asked
in
Probability
Sep 25, 2018
by
Pooja Khatri
171
views
gravner
probability
engineering-mathematics
random-variable
0
votes
0
answers
124
Probability - Gravner-65.a
A biologist needs at least $3$ mature specimens of certain plant. The plant needs a year to reach maturity; once a seed is planted, any plant will survive for the year with probability $1/1000$ (independently of other plants). The biologist ... ) Write down the exact expression for the probability that the biologist will indeed end up with at least $3$ mature plants.
Pooja Khatri
asked
in
Probability
Sep 25, 2018
by
Pooja Khatri
206
views
gravner
probability
engineering-mathematics
random-variable
0
votes
0
answers
125
Probability - Gravner-64.d
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3. (d) Find an expression for $P(Y>10)$.
Pooja Khatri
asked
in
Probability
Sep 25, 2018
by
Pooja Khatri
328
views
probability
gravner
engineering-mathematics
random-variable
0
votes
0
answers
126
Probability - Gravner-64.c
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3. (c) Find an expression $P$($X\geqslant 6$).
Pooja Khatri
asked
in
Probability
Sep 25, 2018
by
Pooja Khatri
167
views
probability
gravner
engineering-mathematics
random-variable
0
votes
0
answers
127
Probability - Gravner-64.b
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3. (b) Write down the probability mass function of Y.
Pooja Khatri
asked
in
Probability
Sep 25, 2018
by
Pooja Khatri
264
views
gravner
random-variable
probability
engineering-mathematics
0
votes
0
answers
128
Probability - Gravner-64.a
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3. (a) Write down the probability mass function of X.
Pooja Khatri
asked
in
Probability
Sep 25, 2018
by
Pooja Khatri
566
views
gravner
probability
engineering-mathematics
random-variable
0
votes
0
answers
129
Probability - Gravner-63
You roll a die, your opponent tosses a coin. If you roll $6$ you win; if you do not roll $6$ and your opponent tosses Heads you lose; otherwise, this round ends and the game repeats. On the average, how many rounds does the game last?
Pooja Khatri
asked
in
Probability
Sep 25, 2018
by
Pooja Khatri
278
views
probability
gravner
engineering-mathematics
random-variable
0
votes
0
answers
130
Probability - Gravner-62
Assume a crime has been committed. It is known that the particular has certain characteristics, which occur with a small frequency $p$ (say,10-8) in a population of size $n$ say (108). A person who matches these characteristics has been found at random( ... security ) and , since $p$ is so small charged with the crime. There is no other evidence. What should the defense be?
Pooja Khatri
asked
in
Probability
Sep 25, 2018
by
Pooja Khatri
101
views
random-variable
probability
gravner
engineering-mathematics
0
votes
0
answers
131
Probability - Gravner-61
Suppose that the probability that a person is killed by lighting in a year is, independently, $1/(500)$ million. Assume that the US population is $300$ million.
Pooja Khatri
asked
in
Probability
Sep 25, 2018
by
Pooja Khatri
144
views
probability
gravner
engineering-mathematics
random-variable
0
votes
0
answers
132
Probability - Gravner-60
Denote by $d$ the dominant gene and by $r$ the recessive gene at a single locus. Then $dd$ is called the pure dominant genotype, $dr$ is called hybrid, and $rr$ the pure recessive genotype. The two genotypes with at least one dominant gene, $dd$ and $dr$, result in the phenotype of the dominant gene, while $rr$ results in a recessive phenotype.
Pooja Khatri
asked
in
Probability
Sep 25, 2018
by
Pooja Khatri
116
views
probability
gravner
engineering-mathematics
random-variable
0
votes
0
answers
133
Probability - Gravner-59
Let $X$ be the number shown on a rolled fair die. Compute EX,E(X2), and Var(X).
Pooja Khatri
asked
in
Probability
Sep 25, 2018
by
Pooja Khatri
137
views
probability
gravner
engineering-mathematics
random-variable
0
votes
1
answer
134
Probablity-Gravner-58
Let $X$ be a random variable with $P(X=1) =0.2,P(X=2)=0.3$, and $P(X=3)=0.5$. What is the expected value of $X$?
Pooja Khatri
asked
in
Probability
Sep 25, 2018
by
Pooja Khatri
273
views
probability
engineering-mathematics
gravner
random-variable
0
votes
0
answers
135
Gate 18 question
Let $X_1, X_2, X_3, X_4$ be independent exponential random variables with mean $1$, $\frac{1}{2}$,$\frac{1}{3}$,$\frac{1}{4}$ respectively. Then Y = min($X_1, X_2, X_3, X_4$) has exponential distribution with mean equal to .
Koushik Sinha 2
asked
in
Probability
Sep 17, 2018
by
Koushik Sinha 2
259
views
random-variable
2
votes
2
answers
136
ISI2016-MMA-9
Suppose $X$ and $Y$ are two independent random variables both following Poisson distribution with parameter $\lambda$. What is the value of $E(X-Y)^2$ ? $\lambda$ $2 \lambda$ $\lambda^2$ $4 \lambda^2$
go_editor
asked
in
Probability
Sep 13, 2018
by
go_editor
854
views
isi2016-mmamma
probability
random-variable
poisson-distribution
expectation
6
votes
0
answers
137
Random Variable
$\mu =E\left ( X \right )$ $\sum P\left ( x \right )=1$ where $x$ 1 2 ... $P(x)$ Standard deviation= $\sigma$ =$\sqrt{\frac{1}{N-1}\sum_{i=1}^{N}\left ( x_{i}-\bar{x} \right )^{2}}$ [for large data like population , ... are correct and important ? Is anything missing plz tell me?? Can someone also derive (i),(ii),(iii) points, I am not getting proper reason behind them Plz check it
srestha
asked
in
Probability
Sep 2, 2018
by
srestha
2.4k
views
probability
random-variable
0
votes
1
answer
138
Random Variable
$1)$ Let $X\sim exp\left ( \lambda \right )$. Find $E\left ( X \right )$ $2)$ Is the value of pdf and $E\left ( X \right )$ is same?
srestha
asked
in
Probability
Sep 2, 2018
by
srestha
255
views
probability
random-variable
1
vote
1
answer
139
Probability (Expected value and Variance)
Find the expected value and the variance of the number of times one must throw a die until the outcome 1 has occurred 4 times.
Mk Utkarsh
asked
in
Probability
Aug 30, 2018
by
Mk Utkarsh
3.3k
views
probability
random-variable
0
votes
2
answers
140
Uniform Random variable-Self Doubt
I was reading the uniform random variable from sheldon ross it is given that X is a uniform random variable on the interval $(\alpha,\beta)$ ... My query is how they derived the distribution function from the density function?
Ayush Upadhyaya
asked
in
Probability
Jul 8, 2018
by
Ayush Upadhyaya
712
views
random-variable
probability
0
votes
0
answers
141
Probability-Sheldon Ross(Self Doubt)
I was reading probability from Sheldon Ross and found below example. A purchaser of electrical components buys them in lots of size 10. It is his policy to inspect 3 components from a lot and to accept the lot if all the 3 are nondefective. If 30 percent of ... why they have multiplied it with $\frac{3}{10}$ in the first part and $\frac{7}{10}$ in the second?
Ayush Upadhyaya
asked
in
Probability
Jul 7, 2018
by
Ayush Upadhyaya
1.6k
views
probability
sheldon-ross
random-variable
0
votes
0
answers
142
Universality of Uniform
According to Universality of Uniform , We can get from the uniform distribution to the other distributions and also from other distributions back to the uniform distribution. Please explain how we would simulate from one distribution to other distribution ?
ankitgupta.1729
asked
in
Probability
May 6, 2018
by
ankitgupta.1729
718
views
random-variable
uniform-distribution
0
votes
0
answers
143
Probability and random variable
Consider the sets $A_1, A_2, A_3 \dots A_m$ each a subset of size $k$ of $\{1,2,3, \dots , n\}$. If in a 2-colouring of $\{1,2,3, \dots , n\}$ no set $A_i$ is monochromatic, then show that $ m < 2^{k-1}$.
dd
asked
in
Set Theory & Algebra
Apr 27, 2018
by
dd
376
views
probability
random-variable
combinatorics-iitb
0
votes
2
answers
144
Maths: Probability Distribution
Suppose X is a uniform random variable between 0.50 and 1.00. What is the probability that a randomly selected value of X is between 0.55 and 0.60 or between 0.75 and 0.85? A. 0.00 B. 0.15 C. 0.60 D. 0.30
blind00x
asked
in
Probability
Apr 22, 2018
by
blind00x
677
views
engineering-mathematics
probability
random-variable
2
votes
3
answers
145
ISI-2014-11
Let $X_1,X_2,X_3,X_4$ be i.i.d. random variables each assuming the value $1$ and $-1$ with probability $\dfrac{1}{2}$ each. Then, the probability that the matrix $\begin{pmatrix}X_1 &X_2\\ X_3 &X_4\end{pmatrix}$ is nonsingular equals $1/2$ $3/8$ $5/8$ $1/4$
jjayantamahata
asked
in
Probability
Mar 15, 2018
by
jjayantamahata
683
views
isi2014
probability
random-variable
1
vote
1
answer
146
Sheldon Ross Normal Variable
In the below question my query is for (a) part When we are calculating $P\left \{ \frac{-1}{3}< Z< \frac{2}{3} \right \}$ I know that the normal variable X is converted to standard normal variable and then we look for values in normal table but I want to know how the third step came? Please explain anyone.
Ayush Upadhyaya
asked
in
Probability
Dec 11, 2017
by
Ayush Upadhyaya
530
views
probability
sheldon-ross
random-variable
0
votes
1
answer
147
Random Variables
Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed 6 times. What are possible values of X?
hem chandra joshi
asked
in
Mathematical Logic
Dec 3, 2017
by
hem chandra joshi
574
views
random-variable
2
votes
2
answers
148
A First Course in Probability- Sheldon Ross 8th Edition Random Variables Example 1b
Three balls are to be randomly selected without replacement from an urn containing 20 balls numbered 1 through 20. If we bet that at least one of the balls that are drawn has a number as large as or larger than 17, what is the probability that we win the bet?
Bhunesh Singh
asked
in
Probability
Nov 10, 2017
by
Bhunesh Singh
896
views
probability
random-variable
1
vote
2
answers
149
Discreate Random Variable (Rose_8th Edition)
Three balls are to be randomly selected without replacement from an urn containing 20 balls numbered 1 through 20. If we bet that at least one of the balls that are drawn has a number as large as or larger than 17, what is the probability that we win the bet? ... X=1) + P(X=2) + P(X=3) = 0.17192 but the answer is 0.508 what is wrong with this approach.
Shubhanshu
asked
in
Combinatory
Jul 18, 2017
by
Shubhanshu
1.9k
views
probability
engineering-mathematics
random-variable
49
votes
7
answers
150
GATE CSE 2017 Set 2 | Question: 31
For any discrete random variable $X$, with probability mass function $P(X=j)=p_j, p_j \geq 0, j \in \{0, \dots , N \}$, and $\Sigma_{j=0}^N \: p_j =1$, define the polynomial function $g_x(z) = \Sigma_{j=0}^N \: p_j \: z^j$. For a certain ... . The expectation of $Y$ is $N \beta(1-\beta)$ $N \beta$ $N (1-\beta)$ Not expressible in terms of $N$ and $\beta$ alone
Arjun
asked
in
Probability
Feb 14, 2017
by
Arjun
16.0k
views
gatecse-2017-set2
probability
random-variable
difficult
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