Thread: Basic question on probability distributions

Hello,

I finished my statistics assignment. I am not sure about a couple of questions in this assignment

Bellow are the questions and my answers. Could someone comment on them please?

Thanks!

Question 1 - http://img98.imageshack.us/img98/8101/questionub5.gif


Answer to Question 1:


(a) It is a valid probability distribution. As p(x) is non-negative for all x and the sum
of p(x) over all possible values of x is 1.0. e.g. 0.41+0.32+0.16+0.08+0.02+0.01 = 1.0

(b) 0.08 + 0.02 + 0.01 = 0.11. This is 11% of seconds.

(c) μ = 0*0.41+1*0.32 + 2*0.16 + 3*0.08 + 4*0.02 + 5*0.01 = 1.01 hits per second.

(d) Variance, σ2 = 0.41*(0-1.01)^2+ 0.32*(1-1.01)^2 + 0.16*(2-1.01)^2 + 0.08*(3-1.01)^2 +0.02*(4-1.01)^2 + 0.01*(5-1.01)^2 = 1.2299.
Hence, standard deviation, σ = √1.2299 = 1.11 hits per second.

(e) For two independent events A and B probability is given by P(A) and P(B) = P(A)P(B)
Thus, for 4 independents events when no calls arrive is calculated by
0.41*0.41*0.41*0.41 = 0.028

Question 2 - http://img365.imageshack.us/img365/2...estion1ua0.gif


Answers to Question 2:
(a)

This experiment does not exhibit the properties of binomial experiment. As the number of trials is not fixed.

(b)

Assuming that a piglet is considered under weight below a specified weight, then this experiment can follow binomial distribution.

-The experiment consists of fixed trials.
-Each experiment results in two outcomes. Each trial has under weight piglet or does not have underweight piglet.
-The probability of success is constant from trial to trial.
-The trials are independent; that is, getting under weight piglet in one trial does not affect whether we get under weight piglet in other trials.

(c)

Assuming probability of children of pre-primary school age who are left-handed is known, then this experiment can follow binomial distribution. Because:

-The number of trials is fixed;
-The fact that a child is left-handed will not influence whether or not next child selected is left-handed. Each observation is independent.
-Each experiment results in two outcomes: left-handed or right-handed.
-Assumed probability of being left-handed is constant for all children who belong to pre-primary group age.

Originally Posted by alexgnnn

Hello,

I finished my statistics assignment. I am not sure about a couple of questions in this assignment

Bellow are the questions and my answers. Could someone comment on them please?

Thanks!

Whci answers are you unsure about?

In 2 (b) and (c) do you know p .....?

Originally Posted by mr fantastic

Whci answers are you unsure about?

In 2 (b) and (c) do you know p .....?

Thanks for your reply.

Unsure about the first and last part of the first question.

Unsure about all of parts to the 2nd question. Screenshot to the 2nd is provided. So what's given is in the question (see the url link)

Originally Posted by alexgnnn

Thanks for your reply.

Unsure about the first and last part of the first question.

Unsure about all of parts to the 2nd question. Screenshot to the 2nd is provided. So what's given is in the question (see the url link)

I'm aware of that. The question was something for you to consider, not to provide me with clarification.

Originally Posted by mr fantastic

I'm aware of that. The question was something for you to consider, not to provide me with clarification.

Feel free not to comment at all.