Statistics and Probability Answers

The table below gives two samples selected from 10 supermarkets of the weekly sales of a popular soft drink. The first sample gives the details for a normal shelf display of the product, while the second sample gives the details for an end-aisle shelf display. Assuming equal variances, establish, at the 5% level of significance, whether there is a statistically significant difference in the mean weekly sales for the two display locations.
Normal display :22,34,52,62,30,40,64,84,56,59
END AISLE DISPLAY: 52,71,76,54,67,83,66,90,77,84

three numbers are selected at random from the numbers 1 to 100. find the probability that they are in A.P?

letters of the word messenger are arranged. find the probability that all the 'S's are together. also find the probability that they are never together

A poll finds that 57% of the population approves of the job that the President is doing; the poll has a margin of error of 2% (assuming a 95% degree of confidence).
What is the 95% confidence interval for the true population percentage that approves of the President's performance?

If FX (x)=[1-e^(-αx) ]U(x-c)). Find fx (x ).

If the r.v. X is X is N(0,2).find P(1≤x≤2│x≥1).

If X and Y are i.i.d r.v.s with 〖fx (x)=α∙e〗^(-αx) u(x) and 〖fY (y)=α∙e〗^(-αy) u(y). Find the pdf fz (z) for Z=2X+Y.

Let fX (x)=1/3 X[U(x)-U(x-2]+1/3 δ(x-1). Find
The expected value E[X]. B. the variance σx^2.

given the following Y=X∙H, where X and H are two random variables with pdf
fX (x)=1/x e^(x^2 ) ,x≥0 ,and fH (h)=1/h e^(〖-3h^2〗^ )
What is the pdf fy|X (y|x)?
What is the pdf fY (y)?

Waiting times at a doctor office are normally distributed with a mean of 35 minutes, and a standard deviation of 10 minutes. What is the chance a patient would have to wait over 50 minutes?