Question

STAT help please

1. Suppose X has normal distribution with mean 5 and variance 1. Find the probability that 5 will be in the random interval (X-1,X+1).

2. Suppose that X has uniform distribution on the interval [0,1]. Find the probability that 1/2 will be in the random interval (X - 1/4, X + 1/4).

3. Suppose X has normal distribution with mean 5 and variance 1. Find the probability that the random variable 2X will be in the random interval (X-1 ,X+1).

Answer 1

\[P(X-1<5<X+1)\]
\[=P(-1<5-X<1)\]
\[=P(-6<-X<-4)\]
\[=P(4<X<6)=\cdots\]