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!

Quote:

Question 1 -

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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

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Question 2 -

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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.