Suppose that a random variable X has a pdf
f(x) = ke^(-3x^2+6x-5), -infinity < x <...
Suppose that a random variable X has a pdf
f(x) = ke^(-3x^2+6x-5), -infinity < x < infinity
(a) Find k.
(b) Find the mean and variance of X.
(c) Find the probability that X is between 1 and 1.5.
Suppose that a random variable X has a pdf
f(x) = ke^(-3x^2+6x-5), -infinity < x < infinity
(a) Find k.
(b) Find the mean and variance of X.
(c) Find the probability that X is between 1 and 1.5.
Suppose that a random variable X has a pdf
f(x) = ke^(-3x^2+6x-5), -infinity < x < infinity
(a) Find k.
(b) Find the mean and variance of X.
(c) Find the probability that X is between 1 and 1.5.
Suppose that a random variable X has a pdf
f(x) = ke^(-3x^2+6x-5), -infinity < x < infinity
(a) Find k.
(b) Find the mean and variance of X.
(c) Find the probability that X is between 1 and 1.5.
5. Consider a random variable with a piecewise-constant PDF f(x)
= 1/2, 0 < x ? 1, 1/8, 1 < x ? 3, 1/12 , 3 < x < 6.
Design the simulation algorithm using the inverse-transform
method.
1. The random variable X has probability density function: f(x)
= ( ke−x 0 ≤ x ≤ ln 5 4 0 otherwise Part a: Determine the value of
k. Part b: Find F(x), the cumulative distribution function of X.
Part c: Find E[X]. Part d: Find the variance and standard deviation
of X. All work must be shown for this question. R-Studio should not
be used.
The random variable X has probability density function: f(x) =
ke^(−x) 0 ≤ x ≤ ln (5/4) 0 otherwise Part a: Determine the value of
k. Part b: Find F(x), the cumulative distribution function of X.
Part c: Find E[X]. Part d: Find the variance and standard deviation
of X. All work must be shown for this question.
For the function f(x) = x^2 +3x / 2x^2 + 6x +3 find the
following, and use it to graph the function.
Find: a)(2pts) Domain
b)(2pts) Intercepts
c)(2pts) Symmetry
d) (2pts) Asymptotes
e)(4pts) Intervals of Increase or decrease
f) (2pts) Local maximum and local minimum values
g)(4pts) Concavity and Points of inflection and
h)(2pts) Sketch the curve
Let X be a continuous random variable with pdf: f(x) = ax^2 −
2ax, 0 ≤ x ≤ 2
(a) What should a be in order for this to be a legitimate
p.d.f?
(b) What is the distribution function (c.d.f.) for X?
(c) What is Pr(0 ≤ X < 1)? Pr(X > 0.5)? Pr(X > 3)?
(d) What is the 90th percentile value of this distribution?
(Note: If you do this problem correctly, you will end up with a
cubic...
Suppose we have the following pdf for the random variable X
f(x) ={x 0<=x<=1
c/x^2 1<=x<= infinity
0 otherwise
}
(a) 2 points Find the value c such that f(x) is a valid pdf.
(b) 3 points Find the cdf of X.
(c) 1 point Find the 75th percentile of X.
f(x)= 1/3x^3 + 5/2x^2 - 6x + 4; [-9,3]
The absolute maximum value is ____ at x = ___
(Use comma to separate answers as needed. Round to two
decimal places as needed)
The absolute minimum value is ____ at x = ___
(Use comma to separate answers as needed. Round to two
decimal places as needed)