Question

Suppose that a random variable X has the distribution (pdf) f(x) =kx(1 -x^2) for
0 < x < 1 and zero elsewhere.
a. Find k.
b. Find P(X >0. 8)
c. Find the mean of X.
d. Find the standard deviation of X.

2. Assume that test scores for all students on a statistics test are normally
distributed with mean 82 and standard deviation 7.
a. Find the probability that a single student scores greater than 80.
b. Find the probability that the mean of a sample of 8 students in greater
than 80.

3. The probability distribution for the number of siblings (Y) for students in a statistics
class is given by

y 0 1 2 3 4
p(y) 0.3 0.3 0.2 0.15 ?
a. Find the missing probability.
b. Find the mean of the distribution.
c. Find the variance of the distribution.

4. A fair die is rolled 120 times. Let Y represent the number of times a three comes
up.
a. Find the P(Y =19). Do this one by hand using the appropriate formula.
b. Find P(19 <= Y <=21).
c. Give the mean and variance of Y.

Answer 1