Note: The PMF of the binomial distribution is

where n is the number of trials and p is the probability of success on each trial.

 

You do not have to compute any figures for this homework assignment.

 

 

 

Wow...it's been so long since I did stats in college or did basic probability...is the sum question just one of those with i = x to y and then the binomial expression after, or am I missing something?

P.S. Any tips on how to type math expressions would be great!

[NEAS: Correct. For math expresssions, you can sometimes copy from Word to the discussion forum.]

No help on the equations but the sum i = x to y sounds right to me and then just use the binomial expression.

[NEAS: Fox’s textbook, like much modern statistical analysis, emphasizes the conditional distribution of the response variable (the dependent variable). Yes, this is a binomial distribution, which is used again in later modules. When the response variable is a probability, the proper conditional distribution is binomial, not normal. In practice, if the number of observations is large enough, the probability is close to 50%, and the observed values are near the mean, the normal distribution is a good approximation. The exact solution uses the binomial distribution. You should be familiar with the binomial distribution for the actuarial exams. If you want to check a formula for any statistical distribution, check the distribution in Wikipedia, which gives all the formulas and expressions you might need.]

Are the first section of questions (below) meant to be an algebraic expression or a numeric solution?

 

If all judges grant leave in 25% of cases, and the differences among judges are random fluctuations, what is the probability a judge (Desjardins) grants leave in 49% or more of cases?

 

 If all judges grant leave in 25% of cases, and the differences among judges are random fluctuations, what is the probability that a judge (Pratte) grants leave in 9% or fewer of cases?

I believe that we are only intended to provide the algebraic expression. I think that these are supposed to be *like* significance tests which are covered later on.

I agree with others, this question was reasonable, but also totally out of left field.

 

When the overview instructs me to know a certain formula is it implying that I need to memorize said formula?

For those who are like me and have to take that extra step:

Part A) Prob(N>=23) ~ 0.03389%

Part B) Prob(N<=5) ~ 0.1768%

I did this using excel to calculate each probability for N from 23 through 47: 

=FACT(M)/(FACT(M-N)*FACT(N))*(.25)^N*(.75)^(M-N)

and just sum the probabilities together. If you spread the range from 0-47, you will see that the total probability is equal to 1.00. To get part B, repeat with M=57.

Hey there,

I'm not sure whether I understand the first set of two questions correctly. Am I suppose to use a normal approximation or a binomial expression? If it is that I have to use a normal approx, then I'm assuming 25% is the average and i have to calculate the standard deviation from the table? Or if it's binomial, then would I have to assume a random number of trials and then use 25% as the probability of success and calculate the probability from there?

Any help would be appreciated, thanks!

[NEAS: Use a binomial distribution. Table 1.1 gives the number of cases for the two judges (Desjardins and Pratte).]

Not sure about this.Please explaine me………..