Download 1) A coin is tossed 4 times. Let X represent the difference between

1) A coin is tossed 4 times. Let X represent the difference between the number of
heads and the number of tails obtained. What is the probability distribution of X?
2) An insurance salesman will make two calls to sell insurance policies. The first call
will lead to a sale with probability 0.3, and the second will lead independently to a
sale with probability 0.6. Any sale will lead to a sale of a policy which costs SR
1000, or a a policy which costs SR 500, with equal probabilities.
a) Determine the probability mass function of X, the total value of all sales.
b) Find the expected value of X.
3) If the distribution function of X is given by
0 x  0
1

0  x 1
2
3
 1 x  2
 5
F (x )   4
5 2  x  3

 9 3 x  7
10
2

1 x  7

2
a) Calculate the probability mass function of X.
b) Find the expected value and the variance of X.
4) A multiple choice test with 10 questions each of which has 4 possible answers.
What is the probability that a student would get at least 8 correct answers just by
guessing?
5) Two balls are chosen at random from a box containing 5 black and 5 white balls.
If they are the same color, then you win 2 riyals; if they are different colors then
you lose 1.5 riyals.
a) What is the expected value of your winnings?
b) What is the variance of your winnings?
6) If E(X) = Var(X) = 2, find
a) E(3+X)2
b) Var(1+2X)
7) Electrical engineers use the following scheme to send messages. A message
consists of a word that is either a 0 or 1. However because of random noise in the
channel, a 1 that is transmitted can be received as a 0 and vice versa, each with
probability 0.05. The scheme of transmission repeats the selected digit 3 times in
succession. At the receiving end, the majority rule will be used to decode.
a) What is the probability that a transmitted 1 will be received as 1.
b) If a message consisting of a 1 followed by 0, is to be transmitted using the
same scheme described above. What is the probability that the message will be
correctly decoded?
8) Pencils produced by a certain company will be defective with probability .02
independently of each other. The company sells the pencils in packages of 12 and
offers a money-back guarantee that at most 1 of the 12 pencils in the package will
be defective. If you buy 5 packages, what is the probability that you will return
exactly 1 of them?
9) Suppose that the number of accidents occurring on a highway each day is a
Poisson random variable with mean equals 3.Find the probability that at least 3
accidents occur today.
10) A batch of 100 items contains 10 that are defective. If a sample of size 5 is drawn
what is the probability that the number of defectives is at most 2?
11) An automated weight monitor can detect underfilled cans of beverages with
probability 0.98. What is the probability it fails to detect an underfilled can for the
first time when it encounters the 10th underfilled can?