Im asking for number 6 not 7 NOTE: II you expect partial credit, I expect to see

Question

Im asking for number 6 not 7

NOTE: II you expect partial credit, I expect to see your work 6) 10-pt. suppose that the random variable X is (continuous) uniformly distributed from 10 to 30 a) Compute the mean of the density function. b) Compute the standard deviation of the density function. Round answer to 2 decimals. c) Convert X-25 into standard units. Round answer to 2 decimals. d) Determine probability that X is equal to 25 e) Determine the probability that X is more than 25. f) Determine the first quartile 7) 1-pt. Either based on the textbook or using the internet, tell me how the "Bernoulli" distribution is related to the Binomial distribution. Use 20 words or less.

Explanation / Answer

For a Uniform distribution we have:

a = 10, b = 30

a. Mean of uniform dist = (b-a)/2 = (30-10)/2 = 10

b. Stdev of uniform dist = (b-a)^2/12 = (30-10)^2/12 = 33.33

c. X = 25, into std units is X-mu / Sigma = (25-10)/33.33 = .45

d. P(X=25) = 0, as there are infinite points, since this is a continous uniform distribution

e. P(X>25) = 1-P(X<=25) = 1- ( 25-10)/(30-10) = .25

f. 1st quartile is = (x-a)/(b-a) = .25

So, (x-10)/(30-10) = .25

x = 10+.25*20 = 15

15 is the 25th percentile or the 1st quartile

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