The random variable X is normally distributed with mean 5 and standard deviation 25. The random variable Y is defined by Y = 2 + 4X. What are the mean and the standard deviation of Y ?

The correct answer is "100".

Explanation:

The given values are:

X (mean) = 5

X (standard deviation) = 25

Variance of X will be:

=

=

The solution of the part first is:

The given equation is :

On putting the value of x in above equation we get ,

So we get the mean of Y is 22

For finding the S.D of Y

So,

variance of Y= Var(2+4X)

As we know that the variance of constant is zero

So, variance (2) =0

⇒

⇒

So,

⇒

We know the variance of constant is zero

So, var(2)=0

⇒

Thus the standard deviation of Y is:

=

=