Suppose that Y is a normally distributed random variable with μ = 10 and σ = 2, and X is an independent random variable, also normally distributed with μ = 5 and σ = 5. Find (a) P(Y  12 and X  4) (b)...

Suppose that Y is a normally distributed random variable with μ = 10 and σ = 2, and X is an independent random variable, also normally distributed with μ = 5 and σ = 5. Find

(a) P(Y
 12 and X
 4)

(b) P(Y
 12 or X
 4)

(c) P(Y
 10 and X
 5)

In a sample of size 5 from a normal distribution, which is more likely: that the sample variance will be less than half the true variance, or that it will be more than twice the true variance?