CSIR NET Mathematics 2024|Standard distribution | 19 April 2024

Let x have a binomial distribution with parameters n and p, where n is an integer greater than 1 and 0 < p < 1

If p (x = 0) = p (x = 1)

Then the value of p is

Lt x ~ B .

Find

Let x₁ and x₂ be iid. Exp(3) random variable. Then

p (x₁ + x₂ > 1) equals

If the joint probability tensity function of (x, y) is given by

Then

If x₁ and x₂ are iid. N(0, 1) random variables then  equals