Thread: Random Variable (Normal Distribution)

Hello,

Struggling to answer the following question:

The random variable Z has the mean -4 and standard deviation 5. Find:
E[3-2Z]
E[(3-2Z)^2]

Now, I think this is a normal distribution, Z~N(-4, 5^2).

And that E(Z) = -4, but as it has more terms in the E[], i'm a little confused on what to do!

Thanks

Originally Posted by MattWT

Hello,

Struggling to answer the following question:

The random variable Z has the mean -4 and standard deviation 5. Find:
E[3-2Z]
E[(3-2Z)^2]

Now, I think this is a normal distribution, Z~N(-4, 5^2).

And that E(Z) = -4, but as it has more terms in the E[], i'm a little confused on what to do!

Thanks

By properties of expected value, .

Now with regards to , there's a quick way to do this using the definition of variances:



But then by properties of variances, . Thus, we can write this as:

.

Once you find , then you should be able to find because we happen to know what is.

Can you proceed?