Sample Test for Stat

Sample Test 1 Questions –Stat 511 Fall 2013

1. A chemical supply company currently has in stock 100lb of a certain chemical, which it sells to customers in 5-lb lots. Let X = the number of lots ordered by a randomly chosen customer, and suppose that X has pmf

x | 1 | 2 | 3 | 4 |

P(x) | .2 | .3 | .3 | .2 |

Compute E(X) and V(X). Then compute the expected number of pounds left after the next customer’s order is shipped, and the variance of the number of pounds left. (Hint: The number of pounds left is a linear function of X.)

2. Twenty-five percent of all telephones of a certain type are submitted for service while under warranty. Of these, 60% can be repaired whereas the other 40% must be replaced with new units. If a company purchases ten of these telephones, what is the probability that exactly two will end up being replaced under warranty?

3. Suppose the number X of tornadoes observed in Kansas during a 1-year period has a Poisson distribution with θ=9

a. Compute

b. Compute

c. Compute

NOTE: look at the Poisson process ideas as well

4. A college professor always finishes his lectures within 2 minutes after the bell rings to end the period and the end of the lecture. Let X = the time that elapses between the bell and the end of the lecture and suppose the pdf of X is

a. Find the value of k. [Hint: Total area under the graph of f(x) is 1.]

b. What is the probability that the lecture ends within 1minutes of the bell ringing?

c. What is the probability that the lecture continues beyond the bell for between 60 and 90 seconds?

d. What is the probability that the lecture continues for at least 90 seconds beyond the bell?

5. Text p.127 Ex68 but change Part (c) to read: calculate the probability that X is at least two given that X is at least one.

6. Text p.162 Ex 33 but change part(c) to read “60% of the mopeds have maximum speed greater than what...