Question

Let the probability density function of the random variable X be f(x) = { e ^2x...

Let the probability density function of the random variable X be f(x) = { e ^2x if x ≤ 0 ;1 /x ^2 if x ≥ 2 ; 0 otherwise}

Find the cumulative distribution function (cdf) 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
2. Let the probability density function (pdf) of random variable X be given by:                           ...
2. Let the probability density function (pdf) of random variable X be given by:                            f(x) = C (2x - x²),                         for 0< x < 2,                         f(x) = 0,                                       otherwise      Find the value of C.                                                                           (5points) Find cumulative probability function F(x)                                       (5points) Find P (0 < X < 1), P (1< X < 2), P (2 < X <3)                                (3points) Find the mean, : , and variance, F².                                                   (6points)
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 ).
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 X be a random variable with probability density function f(x) = { λe^(−λx) 0 ≤...
Let X be a random variable with probability density function f(x) = { λe^(−λx) 0 ≤ x < ∞ 0 otherwise } for some λ > 0. a. Compute the cumulative distribution function F(x), where F(x) = Prob(X < x) viewed as a function of x. b. The α-percentile of a random variable is the number mα such that F(mα) = α, where α ∈ (0, 1). Compute the α-percentile of the random variable X. The value of mα will...
Let X be the random variable with probability density function f(x) = 0.5x for 0 ≤...
Let X be the random variable with probability density function f(x) = 0.5x for 0 ≤ x  ≤ 2 and zero otherwise. Find the mean and standard deviation of the random variable X.
Let the probability density of X be given by f(x) = c(4x - 2x^2 ), 0...
Let the probability density of X be given by f(x) = c(4x - 2x^2 ), 0 < x < 2; 0, otherwise. a) What is the value of c? b) What is the cumulative distribution function of X? c) Find P(X<1|(1/2)<X<(3/2)).
Let X be a random variable with probability density function fX(x) = {c(1−x^2)if −1< x <1,...
Let X be a random variable with probability density function fX(x) = {c(1−x^2)if −1< x <1, 0 otherwise}. a) What is the value of c? b) What is the cumulative distribution function of X? c) Compute E(X) and Var(X).
Let X be a continuous random variable with the following probability density function: f(x) = e^−(x−1)...
Let X be a continuous random variable with the following probability density function: f(x) = e^−(x−1) for x ≥ 1; 0 elsewhere (i) Find P(0.5 < X < 2). (ii) Find the value such that random variable X exceeds it 50% of the time. This value is called the median of the random variable X.
Suppose a random variable X has cumulative distribution function (cdf) F and probability density function (pdf)...
Suppose a random variable X has cumulative distribution function (cdf) F and probability density function (pdf) f. Consider the random variable Y = X?b a for a > 0 and real b. (a) Let G(x) = P(Y x) denote the cdf of Y . What is the relationship between the functions G and F? Explain your answer clearly. (b) Let g(x) denote the pdf of Y . How are the two functions f and g related? Note: Here, Y is...
The random variable X has probability density function: f(x) = ke^(−x) 0 ≤ x ≤ ln...
The random variable X has probability density function: f(x) = ke^(−x) 0 ≤ x ≤ ln 2 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.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT