Statistics and Probability Answers

There are 50 fields in a village, sown with wheat and each is divided into 8 plots
of equal size. Out of the 50 fields, 5 are selected by SRSWOR method. Again
from each selected field, 2 plots are chosen by SRSWOR method. The yield in
kg/plot recorded is as given in the following table:
Selected Field - Plot-I - Plot-II
1 - 4⋅16 - 4⋅76
2 - 5⋅ 40 - 3⋅52
3 - 4⋅12 - 3⋅73
4 - 4⋅38 - 5⋅67
5 - 5⋅31 - 2⋅59
Estimate the average yield of all the 50 plots.

Determine the value of c so that the following functions represent the joint pmf of
the random variables X and Y .
i) f (x, y) = c(x + y +1), x = 0, 1, 2, 3 and y = 0, 1, 2 .
ii) f (x, y) = c(x^2 + y^2), x = −1, 1 and y = −2, 2

Let A and B be two events associated with an experiment such that 4 P(A) = 0. and
P(A ∪ B) = 0.7 . Compute ) P when (B
i) A and B are mutually exclusive.
ii) A and B are independent.

The amount of apples (in kg) produced per day by 10 orchards are given below:
218.2 179.5 207.3 224.3 213.7
199.7 184.7 194.4 203.5 185.4
Find the first four moments about the mean and the coefficient of kurtosis for the
above data.

3 batteries are chosen at random from 15 batteries from which 5 are defective. Find the probability that:

A) none of the three are defective
B) exaxtly one is defective
C) 2 defective and one nondefective
D)at least one is nondefective.

Please type the solution. Im struggling~~ :( Please help meeeee~ THANK YOUUU~

A and b are equally good tennis players

The following data represents the sale (Rs. 1,000) per month of 3 brands of a
toilet soap allocated among 3 cities:
Cities
Brands A B C
I 42 48 30
II 42 54 57
III 29 42 29
At 5% level of significance, test whether the mean sales of 3 brands are equal.

In a University, 20% of all students are graduates and 80% are undergraduates.
The probability that a graduate student is married is 0.5 and the probability that an
undergraduate student is married is 0.1. One student is selected at random. What
is the probability that (i) he/she is married (ii) the student is a graduate if he/she is
found to be married?

Assuming that it is true that 2 in 10 industrial accidents are due to fatigue, find the
probability that exactly 2 of 8 industrial accidents will be due to fatigue.

Let the sample space be S={1, 2, 3, 4, 5}. Suppose the outcomes are equally likely. Compute the probability of the event E="an even number less than 5