Suppose that it takes students between five and 10 minutes to walk from one clas

ID: 3241772 • Letter: S

Question

Suppose that it takes students between five and 10 minutes to walk from one classroom to another, and that the time is distributed uniformly.

The following graphs apply:

a. What is the value of c, the lower end-point of the interval where the probability density function, pdf, is non-zero?

b. What is the value of d, the upper end-point of the interval where the probability density function, pdf, is non-zero?

c. What is the value of h, shown in the upper graph of the pdf, that makes the function a valid probability distribution?

d. What is the slope of the cdf, m, in the lower graph?

g(x) PDF of Uniform Distribution O G(x) CDF of Uniform Distribution

It is given that the students between five and 10 minutes to walk from one classroom to another, and that the time is

distributed uniformly.

That is time taken by students to walk from one classroom to another follows Uniform ( c = 5, d = 10)

a) So that the value of c, the lower end-point of the interval where the probability density function, pdf, is non-zero is 5

b. and the value of d, the upper end-point of the interval where the probability density function, pdf, is non-zero is 10

c) Since time is continuous variable so it is continuous uniform distribution

So that the value of h = 1/(b - a) = 1/ (10 - 5) = 1/5 = 0.2

d) the slope of the cdf, m, in the lower graph is ( 1 - 0)/ (10 - 5) = 1/5 = 0.2

Because cdf of uniform distribution = (x - a) / (b - a) = (x - 5) / (10 - 5) = (x - 5 )/5 = x/5 - 1

Which is a equation of a straight line as y = mX + n

where slope = m = (1/5) = 0.2

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