Statistics and Probability Answers

In a study, physicians were asked what the odds of breast cancer would be in a woman who was initially thought to have a 1% risk of cancer but who ended up with a positive mammogram result (a mammogram accurately classifies about 80% of cancerous tumors and 90% of benign tumors). Ninety-five (95) out of a hundred physicians estimated the probability of cancer to be about 75%. Do you agree?

It is estimated by an insurance company that 90% of total population of age 40--50

years has good health. Using tree diagram finds the probability that: (i) Non (ii) Only

One (iii) Two (iv) All have good health if 3 persons of such age bracket are selected

at random.

1. Find the appropriate distribution for this question. If there are 13 customers entering a restaurant per 2 minutes on average. Find the probability of having 20 or more customers entering the restaurant in a particular 2 minutes.

A continuous random variable x has the pdf given by

f(x)={ e^-x for x>0

{0,ellsewhere

Find the mean and the standard deviation of

a)x

b)y=e^(3/4)x

An acher shoots an arrow on a target. The distance of the arrow from the center of the target is a random variable x,whose pdf is given by

f(x)={k(3+2x-x²) if x<or equal to 3

{0 if x>3

find the values of the constant k,also find the mean and standard deviation of X

The lifetime of new engines T years has a continuous pdf f(t)={d/t² if x>or equal1

{0,elsewhere

the value of the constant d,hence determine the mean and standard deviation T

A continuous random variable x has the pdf given by

f(x)={k(1-x) for 0<x<1 both inclusive

{o,elsewhere

find t,the value of the constant k. Also find the mean and the variance of x

A continuous random variable M has a pdf given by f(m)={k(1-m/10)for m<or equal to 10

{0,elsewhere

find the value of the constant k,the mean and the variance of x

The pdf of a continuous random variable R is given by f(r)={kr for 0<x<4 both inclusive

{0,elsewhere

a)determine c hence compute p(10<r<2)both inclusive, E(r) and var(r)

A fair six sided die has "1" on the face ,"2" on two of its faces and "3".on the remaining three faces. The die is rolled twice. If T is the total score write down the probability distribution of T hence determine

a) the probability that T is more than 4

b)The mean and the variance of T