Statistics and Probability Answers

An independent identically distributed sample size of 3 is chosen from a continuous distribution having density function f(x)=2x,0<x<1, 0 e.w . Find the probability that every member of the sample is less than the median of the distribution.

If Y=aX+b, show that Y has the same coefficient of skewness?

A player tosses two fair coins. He wins $ 2 if 2 head occur and $1 if 1 head occur. On the other hand, he loses $3 ıf no head occurs. Determine the player's expected value and if the game is favorable to the player.

suppose three test kits are tested at random. let D represent the defective test kit and let N represent the non defective test kit. if we let x be the random variable for the number of defective test kits, construct the probability distribution of the random variable X

suppose three test kits are tested at random. let D represent the defective test kit and let N represent the non defective test kit. if we let x be the random variable for the number of defective test kits, construct the probability distribution of the random variable X

The majority of the data is normally distributed if there are enough subjects. For instance, if you collected test scores of only a few honor students, the data will most likely not be normally distributed because you would have a sample that did not represent the entire population. But the identical test scores (for honor students) collected from all schools in a state will result in a normal distribution.

Identify an example of a population that you would expect to be normally distributed. Explain why you believe it would be normally distributed. Then, describe a subset of the population you identified and explain why it would not be normally distributed and what the distribution would look like.

Rolling a Die If a die is rolled one time, find

these probabilities.

a. Getting a 2

b. Getting a number greater than 6 0

c. Getting an odd number

d. Getting a 4 or an odd number

e. Getting a number less than 7 1

f. Getting a number greater than or equal to 3

g. Getting a number greater than 2 and an even number

) Let X be a binomial variate with n =100, p = .1.0 Find the approximate value of

P 10( ≤ X ≤12) using: (5) 

 (i) normal distribution 

 (ii)poisson distribution 

 [You may like to use the following values. 

 P(Z ≤ 67.0 ) = .0 7486, P(Z ≤ 33.0 ) = .0 6293, P(Z ≤ )0 = ]

b) For 25 army personnels, line of regression of weight of kidneys (Y) on weight of 

heart (X ) is Y = .0 399X + .6 934 and the line of regression of weight of heart on 

weight of kidney is X − .1 212Y + .2 461= .0 Find the correlation coefficient between 

X and Y and their mean values.