Statistics and Probability Answers

Let the pdf of X be given by

f(x) = 0.25 exp((0.25x), x > 0

Show that E(X) = 4 and V ar(X) = 16

Mr. A draws a ticket from a box containing 2 bad, 10 good and 5 very good tickets. If Mr. B draws the next ticket, what is his chance of a better performance than Mr. A?

In an attempt to compare the performance of students with more than one electronic gadget and those with only one or none, the mean grades of students and standard deviations were taken and shown in the table below.

. Let the probability distribution function of X be given by f(x) = 0.25 exp(−0.25x), x > 0 Show that E(X) = 4 and V ar(X) = 16

A chicken rice chain store conducted a taste survey before marketing its’

newly tasted chicken rice. The results of the survey showed that 85% of the

people who tried this new chicken rice liked it. Excited by this result, the

chain store decided to market this newly taste chicken rice. On a certain day,

ten customers bought this chicken rice for the first time.

Find the probability that exactly four of the customers will like the

chicken rice.

Experts claim that 5% of crimes are committed by women. Is there enough evidence to reject the claim if in a sample of 50 crimes, 5 were committed by women? Use 5% significant level.

A lottery that pays off Php 300 000. 00 is made available for 10 000 000 tickets. Each ticket costs Php 50.00. Suppose the variable X gives the net winnings from paying lottery. What is the expected gain for joining the lottery with only one ticket?

Binomial Distribution

In a survey, 25% of the people interviewed said that they bought their refrigerator during the last six months. If eleven people are selected at random, find the probability that exactly six of these people bought their refrigerator during the last six months.

In a survey, 25% of the people interviewed said that they bought their refrigerator during the last six months. If eleven people are selected at random, find the probability that exactly six of these people bought their refrigerator during the last six months.

1-Let n X₁, X₂ ....X_n be random sample of size n from a distribution with probability

density function f(x,q)=qx^q-1

0, else where.

Obtain a maximum likelyhood

estimator of q.

2- Let , X₁, X₂ Xn be independently and identically distributed b(1, p) random

variables. Obtain a confidence internal for p using Chebychev’s inequality