5. Consider a random variable with a piecewise-constant PDF f(x) = 1/2, 0 < x ?...

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.

Expert Solution

orchestra answered 2 years ago

Let X be a continuous random variable with pdf: f(x) = ax^2 − 2ax, 0 ≤...

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<=...

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.

Let X be a exponential random variable with pdf f(x) = λe−λx for x > 0,...

Let X be a exponential random variable with pdf f(x) = λe−λx for x > 0, and cumulative distribution function F(x). (a) Show that F(x) = 1−e −λx for x > 0, and show that this function satisfies the requirements of a cdf (state what these are, and show that they are met). [4 marks] (b) Draw f(x) and F(x) in separate graphs. Define, and identify F(x) in the graph of f(x), and vice versa. [Hint: write the mathematical relationships,...

Let X be a uniform random variable with pdf f(x) = λe−λx for x > 0,...

Let X be a uniform random variable with pdf f(x) = λe−λx for x > 0, and cumulative distribution function F(x). (a) Show that F(x) = 1−e −λx for x > 0, and show that this function satisfies the requirements of a cdf (state what these are, and show that they are met). [4 marks] (b) Draw f(x) and F(x) in separate graphs. Define, and identify F(x) in the graph of f(x), and vice versa. [Hint: write the mathematical relationships,...

2. Let X be a continuous random variable with PDF ?fx(x)= cx(1 − x), 0 <...

2. Let X be a continuous random variable with PDF ?fx(x)= cx(1 − x), 0 < x < 1, 0 elsewhere. (a) Find the value of c such that fX(x) is indeed a PDF. (b) Find P(−0.5 < X < 0.3). (c) Find the median of X.

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 <...

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 <...

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 <...

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.

a. Consider the following distribution of a random variable X X – 1 0 1 2...

a. Consider the following distribution of a random variable X X – 1 0 1 2 P(X) 1/8 2/8 3/8 2/8 Find the mean, variance and standard deviation b. There are 6 Republican, 5 Democrat, and 4 Independent candidates. Find the probability the committee will be made of 3 Republicans, 2 Democrats, and 2 Independent be selected? c. At a large university, the probability that a student takes calculus and is on the dean’s list is 0.042. The probability...

Question

5. Consider a random variable with a piecewise-constant PDF f(x) = 1/2, 0 < x ?...

Solutions

Expert Solution

Related Solutions

Let X be a continuous random variable with pdf: f(x) = ax^2 − 2ax, 0 ≤...

Suppose we have the following pdf for the random variable X f(x) ={x 0<=x<=1 c/x^2 1<=x<=...

Let X be a exponential random variable with pdf f(x) = λe−λx for x > 0,...

Let X be a uniform random variable with pdf f(x) = λe−λx for x > 0,...

2. Let X be a continuous random variable with PDF ?fx(x)= cx(1 − x), 0 <...

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 <...

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 <...

a. Consider the following distribution of a random variable X X – 1 0 1 2...