Question

Let a random variable X be uniformly distributed between −1 and 2. Let another random variable Y be
normally distributed with mean −8 and standard deviation 3. Also, let V = 22+X and W = 13+X −2Y .

(a) Is X discrete or continuous? Draw and explain.
(b) Is Y discrete or continuous? Draw and explain.
(c) Find the following probabilities.
(i) The probability that X is less than 2.
(ii) P(X > 0)
(iii) P(Y > −11)
(iv) P

Y < 0 and Y > −9

(iv) P

X > 1 or X < 0

(v) P(X ≥ 2)
(vi) P(Y = 0)
(d) What is the mean of X? µX =
(e) If the standard deviation of X is σX = 0.866, what are the mean and standard deviation of V ?
µV =
σV =
(f) Assuming X and Y are independent, what are the mean and standard deviation of W?
µW =
σW =

Answer 1

It is given that

a) X is a  continuous random variable between -1 and 2. The PDF is .

The PDF is plotted below.

b) Y is a  continuous random variable between and .

The PDF is plotted below.

c) The probabilities are

i)

ii)

iii)

(iv)

d) The mean of uniform random variable X is