Normal Distribution

[Devika]

Suppose X and Y are independent random variables with standard normal distributions. The prob of X < -1 is some p belonging to (0,1). What is the prob of the event X^2 >1 AND Y^3 >1?

[Mauli]

hi devika:)


P(X<-1) =P(X>1) = p ..(since it is symmetricie: normal distri is symmetric.
P(X^2>1)= P(X>1) OR P(X<-1) = P+P = 2P

P(Y^3>1)=P(Y>1)=P
since X and Y are independent
P(X^2>1) *P(Y^3>1)= 2P*P =2P^2

[Devika]

Hii mauli :)

Thank you.