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Stat 210
Fall 2009
Quiz#2

A chemical supply company currently has in stock 100 lb 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) 0.1 0.5 0.3 0.1










Find
a) P(1<=X<=2).
b) Find P(1 c) Compute E(X) , the mode, the median, and V (X).
d) Compute the expected number of pounds left after the next customer’s order is shipped and the variance of the number of pounds left.

2. A quality control inspection system requires that from each batch of items a sample of 15 is selected and tested. If 3 or more of the sample are defective the whole batch is rejected. Assume that the probability of an item being defective is 0.05
a) What is the probability of 3 defectives in the sample?
b) What is the probability of the batch being rejected?


3. Packets are transmitted at a transmission channel at a rate of 1000 pps.
Find
a) The probability that between 500 to 750 packets (inclusive) are transmitted over a period of 2 seconds.
b) The probability that the delay time of a packet is .2 seconds.
c) Given that the delay time of a packet is .25 seconds, find the probability that the delay time exceeds .30 seconds.
d) Find the probability that the number of packets transmitted over a period of 4 seconds exceeds fine.


4. The actual tracking weight of a stereo cartridge that is set to track at 3 g on a particular change can be regarded as a continuous r.v. X with pdf
f(x)=kx^2, 0 =0 otherwise.
a) Sketch the graph of f(x) and find the value of k.
b) Find F(x).
c) What is the probability that the actual tracking weight is greater than the prescribed weight?
d) What is the probability that the actual weight is within .25 g of the prescribed weight?

5. Assume that jobs arrive at the server according to a Poisson process with a rate of 50 jps. Find the following probabilities:
a) The time it takes a job to arrive is 1 second.
b) The time it takes a job to arrive is between .01 to .03 seconds.
c) The time it takes a job to arrive is greater than .02 seconds.