Statistics and Probability Answers

Thirty people, who are of the same age and the same health status, are

insured with the same insurance company. Using life tables, the company

estimates that the probability for a randomly chosen person among these 30

to be alive in 15 years from now is 0:8.

(i) What is the probability that not all 30 people will be alive in 15 years time?

(ii) What is the probability that at least one person will be alive?

The probability that a car is stolen when it is parked overnight in an unsafe

area of a city is 10%. If there are 12 cars parked on a particular street of that

area, what is the probability that during a night

(i) no car is stolen?

(ii) at most two cars are stolen?

(iii) at least nine cars are stolen?

A TV manufacturer claims that the life span of its regular TV sets is longer than 10 years with a standard deviation of 1.5 years. Using a random sample of their 16 TV sets, the average life span is found to be 11.5 years. Test the hypothesis that the TV sets' life span is longer than 10 years at a = 0.01.

A chemical company alleged that the average weight of its bag of chemical is 50 kgs. with a standard deviation of 0.9 kg. A sample of 29 bags was taken and revealed a mean weight of 48.1 kgs. Shall we accept the allegation of the chemical company? Use a = 0.01.

In a public senior high school, a survey conducted last year showed that 25%

of the students’ parents are farmers. This year, a new survey was conducted

randomly on 150 students from the same school. It was found that 63 of them

have parents who are farmers. Test if the claim was higher at α = 0.01 level.

If P (A|B) = 0.5, P (A) = 0.45 and P (B) = ?

Suppose the random variable Y has a normal distribution with an expected value equal to 12 and variance equal to 16. What is the value of k such as that P(X<k)= 0.25

1. Let X₁, X_{2 ,} and X₃ be independent standard normal random variable. If we defined Y₁=X₂, Y₂=X₁+X₂/2 and Y₃=X₁+ X₂ +X₃/3.Then find then joint pdf of Y₁, Y_2, and Y₃ using the Jacobian method?

1.The waiting time, in hour, between successive speeders spotted by a radar units is a continuous random variable with cumulative distribution function

 derive the characteristic function of x and use it to find the mean of x

How many different samples of size 8 can be selected from a population with a size of 12 ?