Statistics and Probability Answers

A coin is tossed twice. Let Z denote the number of heads on

the first toss and W , the total number of heads on the two tosses. If

the coin is unbalanced and a head has a 60% chance of occurring,

find

(a) the joint distribution of W and Z .

(b) the marginal distribution of W .

(c )the marginal distribution of Z .

(d) the probability that at least 1 head occurs. 

Let z be a normal random variable with a mean of 35 and a standard deviation of 4. Determine (z ≤ 1.4)

A sample size of 36 is to be selected from a population that has a mean of µ = 45 and standard deviation s of 10.

1.Find the mean of the sampling distribution

2.Find the standard error of the sampling distribution.

3.What is the probability that this sample mean will be between 40 and 50?

What's the area to the left of z=0?,in other words,What is P(z<0)?

To the right of z=0.3

consider a population consisting of 15,2,12,4,5,8,6,9 and 17.samples of size 5 are drawn from this popular

1. A population of 4 numbers 1,2,4,5

a. List ALL the possible samples of size n=3, which can be drawn with replacement from the population.

b. Construct a sampling distribution of the sample mean.

1. A population consists of 4 numbers 3,7,11,15 of sample size n=2 which can be drawn without replacement from the population.

a. Population mean

b. Population Variance

c. Population standard deviation

d. Mean of the sampling distribution of the sample means

e. Variance of the sampling distribution of the sample means

f. Standard deviation of the sampling distribution of the sample means

A manufacturer of flashlight batteries took a sample of 13 batteries from a day’s production and used them continuously until they failed to work. The life of the batteries in hours until failure is:  342, 426, 317, 545, 264, 451, 1049, 631, 512, 266, 492, 562, 298 . What would you advise if the manufacturer wanted to say in advertisement that these batteries last more than 400 hours?

Let (X,Y) be a two-dimensional continuous random variable with joint P.d.f

𝑓𝑋𝑌

(𝑥,𝑦) = {

2 , 0 < 𝑥 < 𝑦 < 1

0 , 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

Find the marginal distribution for X and Y ?