Math Answers

If X is a random variable such that P (X=x)=Pn,Gp(x) is the pgf f X:n=0,1,2...

Define P[X≥n]=qn.Obtain the pgf of qn in terms of GP(x)

Let X1,X2,...,Xn be independent and identifically distributed random variables each having pdf

f(x)=q^xP .x=0,1,2....

P+q=1

Let Sn=X1+X2+...+Xn.

Obtain the pgf of Sn and find the mean and variance of Sn

Suppose X~Binomial(n,p).Find the pgf of Y=X+1 in terms of GP(x)

X is a random variable such that P(x=n)=Pn n=1,2,...

GP(x)=pgf of x.

Define P(x≤n)=q,and obtain the pgf of qn in terms of GP(x)

Determine how many bit strings of length 6 can be formed, where the last bit is 0 and two consecutive 0s are not allowed.

 1.    The net amount of jam in a standard jar produced by a certain food manufacturer has a normal distribution with mean 340 grams and standard deviation 5 grams.

a.    A jar of jam is rejected if its amount differs from the mean by more than 6 grams.

What is the probability that a randomly selected jar of jam will be rejected?

[4 marks]

b.    Estimate the number of rejected jars if a wholesaler has ordered 500 jars of jam from the manufacturer.

c.     Estimate the number of accepted jars if a wholesaler has ordered 300 jars of jam from the manufacturer.

2Fn>Fn+1 for n>3 true or false

If a set of responses is normally distributed, which of the following statements is NOT true?

1) About 95% of responses fall within two standard deviations of the mean.

2) The data need to be transformed to correct the skew.

3) The scores will be symmetrically distributed around the mean.

4) We can predict the percentage of responses falling within one standard deviations of the mean.

If the rate at 1.25 % effective, how long will Php 5,000 become Php 5,500?

The students of same age group from two different schools were compared for variability in their mathematical skill. A random sample of 25 pupils from one school had a variance of 16 marks while a random sample of 22 pupils from the other school had a variance of 8 marks. Examine if the difference in variability is significant. [F at (24,21) at 5% level of significance is 2.05]