## Quiz #3

Answers are given in the answer boxes below. Scroll down for explantions for the answers (given in red).

Be sure to put your name on this quiz. Write the letters corresponding to the correct answers in the answer boxes below. I'll count your best two out of three (and so you can miss one without penalty).

Question 1 C
Question 2 A
Question 3 B

#### Question 1

If Z is a standard normal random variable, what is the value of P(Z 0)?
• [ A ] 0
• [ B ] (2π)-1/2
• [ C ] 0.5
• [ D ] 0.683
• [ E ] 1
A standard normal distribution is symmetric about 0 --- both P(Z 0) and P(Z 0) equal 1/2.

#### Question 2

If X is a normally distributed random variable having mean 1 and variance 1, so that it's density is
f(x) = (2π)-1/2e-(x - 1)2/2,
what is the value of P(X = 1)?
• [ A ] 0
• [ B ] (2π)-1/2
• [ C ] 0.5
• [ D ] 0.683
• [ E ] 1
The probability that a continuous random variable assumes a value equal to any specific number is equal to 0.

#### Question 3

If U is a uniformly distributed random variable, so that it's density is constant on the interval (0, 2) (i.e., its density equals 1/2 on (0, 2) and equals 0 elsewhere), what is the value of P(U > 1.5)?
(Hint: If you don't get this one right away, I suggest that you sketch the density.)
• [ A ] 0
• [ B ] 0.25
• [ C ] 0.5
• [ D ] 0.75
• [ E ] 1
(I went over this one in class, making use of a sketch I drew on the board.)