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# Statistics Problem Set: Discrete Probability Distribution

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4.182: For each of the following examples, decide whether x is a binomial random variable and explain your decision. (see examples attached).

4.184: Consider the discrete probability distribution shown here.

x 10 12 18 20
p(x) .2 .3 .1 .4

a) Calculate mean, variance and standard deviation.
b) What is P(x < 15)?
c) Calculate mean + or - 2*standard deviation
d) What is the probability that x is in the interval from c.

4.186: Suppose x is a Poisson random variable. Compute p(x) for each of the following cases:
a) Lambda = 2, x = 3
b) Lambda = 1, x = 4
c) Lambda = 0.5, x = 2

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The expert examines discrete probability distribution for statistics problem sets.

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4.182:
a) Yes, x is a binomial random variable. As the event a chip is defective is independent of each other, and the probability that each chip is defective is fixed. In ...

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• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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