Question

A continuous random variable X has pdf ?x(?) = (? + 1) ?^2, 0 ≤ ?...

A continuous random variable X has pdf ?x(?) = (? + 1) ?^2, 0 ≤ ? ≤ ? + 1, Where B is the
last digit of your registration number (e.g. for FA18-BEE-123, B=3).
a) Find the value of a
b) Find cumulative distribution function (CDF) of X i.e. ?? (?).
c) Find the mean of X
d) Find variance of X.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let X be a continuous random variable with probability density function (pdf) ?(?) = ??^3, 0...
Let X be a continuous random variable with probability density function (pdf) ?(?) = ??^3, 0 < ? < 2. (a) Find the constant c. (b) Find the cumulative distribution function (CDF) of X. (c) Find P(X < 0.5), and P(X > 1.0). (d) Find E(X), Var(X) and E(X5 ).
3. Let X be a continuous random variable with PDF fX(x) = c / x^1/2, 0...
3. Let X be a continuous random variable with PDF fX(x) = c / x^1/2, 0 < x < 1. (a) Find the value of c such that fX(x) is indeed a PDF. Is this PDF bounded? (b) Determine and sketch the graph of the CDF of X. (c) Compute each of the following: (i) P(X > 0.5). (ii) P(X = 0). (ii) The median of X. (ii) The mean of X.
2. Let X be a continuous random variable with pdf given by f(x) = k 6x...
2. Let X be a continuous random variable with pdf given by f(x) = k 6x − x 2 − 8 2 ≤ x ≤ 4; 0 otherwise. (a) Find k. (b) Find P(2.4 < X < 3.1). (c) Determine the cumulative distribution function. (d) Find the expected value of X. (e) Find the variance of X
1. There is a 5-digit binary number. Random variable X is defined as the number of...
1. There is a 5-digit binary number. Random variable X is defined as the number of 0's in the binary number. (a) Draw the probability mass function (PMF) for X. (b) Draw the cumulative distribution function (CDF) for X. (c) Using the PMF, find the probability that the 5-digit binary number has at most three 0’s. (d) Using the CDF, find the probability that the 5-digit binary number has at most three 0’s. 2. Now, referring to the PMF that...
A continuous random variable X has the following probability density function F(x) = cx^3, 0<x<2 and...
A continuous random variable X has the following probability density function F(x) = cx^3, 0<x<2 and 0 otherwise (a) Find the value c such that f(x) is indeed a density function. (b) Write out the cumulative distribution function of X. (c) P(1 < X < 3) =? (d) Write out the mean and variance of X. (e) Let Y be another continuous random variable such that  when 0 < X < 2, and 0 otherwise. Calculate the mean of Y.
Let ? be a random variable with a PDF ?(?)= 1/(x+1) for ? ∈ (0, ?...
Let ? be a random variable with a PDF ?(?)= 1/(x+1) for ? ∈ (0, ? − 1). Answer the following questions (a) Find the CDF (b) Show that a random variable ? = ln(? + 1) has uniform ?(0,1) distribution. Hint: calculate the CDF of ?
A random variable X takes values between -2 and 4 with probability density function (pdf) Sketch...
A random variable X takes values between -2 and 4 with probability density function (pdf) Sketch a graph of the pdf. Construct the cumulative density function (cdf). Using the cdf, find ) Using the pdf, find E(X) Using the pdf, find the variance of X Using either the pdf or the cdf, find the median of X
6. A continuous random variable X has probability density function f(x) = 0 if x< 0...
6. A continuous random variable X has probability density function f(x) = 0 if x< 0 x/4 if 0 < or = x< 2 1/2 if 2 < or = x< 3 0 if x> or = 3 (a) Find P(X<1) (b) Find P(X<2.5) (c) Find the cumulative distribution function F(x) = P(X< or = x). Be sure to define the function for all real numbers x. (Hint: The cdf will involve four pieces, depending on an interval/range for x....
5. Let X be a continuous random variable with PDF fX(x)= c(2+x), −2 < x <...
5. Let X be a continuous random variable with PDF fX(x)= c(2+x), −2 < x < −1, c(2−x), 1<x<2, 0, elsewhere (a) Find the value of c such that fX(x) is indeed a PDF. (b) Determine the CDF of X and sketch its graph. (c) Find P(X < 1.5). (d) Find m = π0.5 of X. Is it unique?
Suppose that X is continuous random variable with PDF f(x) and CDF F(x). (a) Prove that...
Suppose that X is continuous random variable with PDF f(x) and CDF F(x). (a) Prove that if f(x) > 0 only on a single (possibly infinite) interval of the real numbers then F(x) is a strictly increasing function of x over that interval. [Hint: Try proof by contradiction]. (b) Under the conditions described in part (a), find and identify the distribution of Y = F(x).
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT