Statistics and Probability Answers

The New York City Housing and Vacancy Survey showed a total of 59,324 rent controlled housing units and 236,263 rent stabilized units built in 1947 or later. For these rental units the probability distributions for the number of persons living in the unit are given.

# of persons Rent controlled rent stabilized
1 .61 .41
2 .27 .30
3 .07 .14
4 .04 .11
5 .01 .03
6 .00 .01

a. what is the expected value of the number of persons living in rent-controlled units?
b. what is the variance of the number of persons living in rent-controlled units?
c. What is the standard deviation of the number of people living in rent-controlled units?
d. What is the expected value of the number of people living in rent-stabilized units?
e. What is the variance of the number of people living in rent-stabilized units?
f. What is the standard deviation of the number of people living in rent-stabilized units?

A few years ago, an analysis of some Wikipedia reference pages noted that the references (citations) at the ends of articles are tend to break over time. That is, the links to the cited articles or sites can’t be followed. It was claimed that 3.9% of these references are incorrect within a span of about one year. If a particular Wikipedia article contains seven references, what is the probability that all seven references are still valid one year later? What assumption must you make in order to calculate this probability?

HOW MANY WAYS ARE THERE TO ROLL EITHER A 4 OR 9 WITH A PAIR OF DICE?

A random sample of 33 individuals has an average age of 28 with a standard deviation of 5.
Find the margin of error for a 98% level of confidence

The 24 students in a class record how long they take to run 100m. The mean time for all the students is 14.8.
A student who ran 100m in 12.7 seconds leaves the school.
Find the mean for the remaining students.

An archer shoots an arrow at a target.
The probability that he will hit the target is 3/4

After the first shot, the target is moved further away from the archer.
The archer shoots a second arrow at the target and the probability that he will hit the
target is now 3/5.(a)Draw a tree diagram for the situation.(b)Calculate the probability that the archer will hit the target with his first shot but miss the target with his second shot(c)calculate the probability that the archer will hit the target at least once if he takes both shots.

You are having three coins. First coin has two tails, second coin has two heads and the third
one has one head and one tail. You choose a coin at random and toss, and get tail. What is the
probability that coin chosen is two tailed coin?
(A) 1/2
(B)1/3
(C)2/3
(D)1/4

In a study of dialysis researchers found that of the three patients who were currently on dialysis 67% had developed blindness and 33% has their toes amputated what kind of display might be appropriate for these data. Explain

the probability that a doctor successfully performs an operation is 80%. what is the probabillity that atleast 3 operations out of 4 conducted by him will be successfull??

1)-Let X be a random variable with density function as follows:

2(x − 1) , 1 < x < 2 f(t) =
0 , elsewhere
• Find the expectation of x, and the variance.
• If g(x) = x2 + x − 2, where x has the same above density function. 1. E(g(x)).
2. E(2)