Math Answers

Box I contains 3 red and 2 blue marbles while Box II contains 2 red and 8 blue marbles. A fair coin is tossed. If the coin turns up heads a marble is chosen from Box I, if it turns up tails a marble is chosen from Box II. Find the probability that a red marble is chosen.

Find the variance and the standard deviation of the sum obtained in tossing a pair of fair dice.

A bank wishing to determine the average amount of time a customer must wait to be served took a random sample of 100 customers and found that the mean waiting time was 2.7 minutes. Assuming that the population standard deviation is known to be 15 minutes, find the %90 confidence interval estimate of the mean waiting time for all the bank’s customers.

lTo determine if a single die is balanced or fair, the die was rolled 600 times. The observed frequencies with which each of the six sides of the die turned up are recorded in the following table:
Face 2 3 4 5 6
observed frequency 114 92 84 101 107 102
Is there sufficient evidence to conclude, at the %5 level of significance, that the die is not fair?

Let Y,X have joint pdf
f xy( x,y)={ 4 ; 0 smaller than equal to x smaller than equal to 1 , 0 smaller than equal to y smaller than equal to 1
and 0 ; otherwise
Find fx ( x) , fy ( y ) ,fx/y ( x/y) ,f y/x ( y/x ) also find E ( X/ Y = y) and E (Y /X = x)

Let X1,X2,............Xn be a random sample from a distribution with density function
f(x, alpha)={ 1/ alpha ; 0 smaller than equal to x smaller than equal to alpha
and 0 ; otherwise
Obtain the maximum likelihood estimator of θ

Let X1,X2,............Xn be a random sample with E(Xi)=m and var( Xi)= sigma^2 for all I= 1,2.....n . show that S^2=1/n-1 sum ( Xi-mean) is an unbiased estimator of sigma^2.

Find the mean and standard deviation of the following frequency distribution. (5) Class Intervals Frequency 6.45 – 7.25 7.25 – 8.05 8.05 – 8.85 8.85 – 9.65 9.65 – 10.45 10.45 – 11.25 11.25 – 12.05 12.05 – 12.85 12.85 – 13.65 7 11 34 67 62 67 33 13 6 Total 300

If in 2009 approximately 30% of the adult population was offline in terms of being able or willing to access the internet.

New data released in May 2016 indicated that this group numbered 5.3 million in the first quarter of 2016.

Using these figures and taking the UK adult population in 2016 to be 52.2 million, calculate the percentage points reduction in offline UK adults indicated by the 2016 data.