Question

3. Compute the variance of X when X is the result of rolling a fair die. 4. Let X be a random variable with density function 1 0<z<1 0 otherwise f(x)= What is the variance of X.

Answer 1

Part A:

Here,

P(i) = 1/6

For all i = 1, 2, 3, ... 6,

E[X] = 1*(1/6) + 2*(1/6) + 3*(1/6) + 4*(1/6) + 5*(1/6) + 6*(1/6)

= 7/2 or 3.5

Now,

E[X²] = Σ i²*P(X=i) (to a total of 6, starting from 1)

Here, i = 1, 2, 3, ... 6,

Or, E[X²] = 1/6 + 2²/6 + 3²/6 + 4²/6 + 5²/6 + 6²/6

Or, E[X²] = 91/6

Now, Var(X) = E[X²] - (E[X])²

= 91/6 - (7/2)²

= 35/12

Part B:

Please find the solution below:

2 티/ 3 3 art 3 44_3 3 I 2

End of the Solution...