MadeEasy Test Series : Probability - Probability

Question

A dice is tossed thrice. A success is getting ‘1 or 6' on a toss. Find the variance of number of successes _. 

Answer  0.66

Comments

Use Binomial distribution:-

In which $Var = npq$

Here, $n = 3, p = \frac{1}{3}, q = \frac{2}{3}$

Pluggin the values into the above formula you will get $Var = 0.66$.

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@Shubhanshu I have not studied mean,variance,expectation....Any resource for the same?

Answer 1

No. of successes:     0                          1                                 2                                  3

Probability:             8/27                   12/27                          6/27                            1/27

E(X) = 0(8/27) + 1(12/27) + 2(6/27) + 3(1/27) = 27/27 = 1;

E(X^2) = 0^2(8/27) + 1^2(12/27) + 2^2(6/27) + 3^2(1/27) = 45/27

V(X) = E(X^2) - [E(X)]^2

V(X) = 45/27 - (1)^2 = 45/27 -1  = 18/27 = 0.66