MATH 3339 Test 2 Question with 100% Verified Answers

MATH 3339 Test 2 Question with 100%
Verified Answers
the area under the graph.

pdf focuses more on..

basically a graph with a straight line where it resembles the integral of the pdf, or the

height.



height cdf = area pdf

the cdf is ...

1

(X ≤ 1) = ∫ x/64*exp(-x^2/128)

0

Using R:

> f <- function(x){x/64*exp(-x^2/128)}

> integrate(f, lower=0, upper=1)

0.007782062 with absolute error < 8.6e-17

E[X] = ∫x*f(x)

2

= ∫ x * (2x/4)

0

Using R:

, > f <- function(x){x*(2*x/4)}

> integrate(f, lower=0, upper=2)

1.333333 with absolute error < 1.5e-14

Let X be the amount of time (in hours) the wait is to get a table at a restaurant. Suppose

the cdf is represented by

F(x)= 0 x<0

x^3/64 0≤x≤4

1 x>4

Use the cdf to determine σX.

- we know sigma is s.d., and variance = sqrt(sd)

- we also know E[X] = ∫ x f(x) and E[X^2] = ∫ x^2f(x)

- VAR[X] = E[X^2] - (E[X])^2

X~Exp

x=9

μ=6

∴ λ = 1/μ = 1/4

P(X ≥ 9)

1 - pexp(9, 1/6)

= 0.2231