Let be the following probability density function f (x) = (1/3)[ e ^ {- x /...

Let be the following probability density function f (x) = (1/3)[ e ^ {- x / 3}] for 0 <x <1 and f (x) = 0 in any other case

a) Determine the cumulative probability distribution F (X)
b) Determine the probability for P (0 <X <0.5)

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Let X has the probability density function (pdf) f(x)={C1, if 0 < x ≤ 1, C2x,...

Let X has the probability density function (pdf) f(x)={C1, if 0 < x ≤ 1, C2x, if1<x≤4, 0, otherwise. Assume that the mean E(X) = 2.57. (a) Find the normalizing constants C1 and C2. (b) Find the cdf of X, FX. (c) Find the variance Var(X) and the 0.28 quantile q0.28 of X. (d)LetY =kX. Find all constants k such that Pr(1<Y <9)=0.035. Hint: express the event {1 < Y < 9} in terms of the random variable X and...

Let the continuous random variable X have probability density function f(x) and cumulative distribution function F(x)....

Let the continuous random variable X have probability density function f(x) and cumulative distribution function F(x). Explain the following issues using diagram (Graphs) a) Relationship between f(x) and F(x) for a continuous variable, b) explaining how a uniform random variable can be used to simulate X via the cumulative distribution function of X, or c) explaining the effect of transformation on a discrete and/or continuous random variable

a. For the following probability density function: f(X)= 3/4 (2X-X^2 ) 0 ≤ X ≤ 2 &nbsp

a. For the following probability density function: f(X)= 3/4 (2X-X^2 ) 0 ≤ X ≤ 2 = 0 otherwise find its expectation and variance. b. The two regression lines are 2X - 3Y + 6 = 0 and 4Y – 5X- 8 =0 , compute mean of X and mean of Y. Find correlation coefficient r , estimate y for x =3 and x for y = 3.

Let f(x) = b(x+1), x = 0, 1, 2, 3 be the probability mass function (pmf)...

Let f(x) = b(x+1), x = 0, 1, 2, 3 be the probability mass function (pmf) of a random variable X, where b is constant. A. Find the value of b B. Find the mean μ C. Find the variance σ^2

Let X1, ..., Xn be i.i.d random variables with the density function f(x|θ) = e^(θ−x) ,...

Let X1, ..., Xn be i.i.d random variables with the density function f(x|θ) = e^(θ−x) , θ ≤ x. a. Find the Method of Moment estimate of θ b. The MLE of θ (Hint: Think carefully before taking derivative, do we have to take derivative?)

1. Let X be a random variable with probability density function fX given by fX(x) =...

1. Let X be a random variable with probability density function fX given by fX(x) = γαγ/ (x + α)^γ+1 , x ≥ 0, 0, x < 0, where α > 0 and γ > 0. (a) Find the cumulative distribution function (cdf) FX of X. (b) Let Y = log(X+α /α) . Find the cdf of Y and identify the distribution. (c) How could a realisation of X be generated from an R(0,1) random number generator? (d) Let Z...

Suppose that X and Y have the following joint probability density function. f (x, y) =...

Suppose that X and Y have the following joint probability density function. f (x, y) = (3/394)*y, 0 < x < 8, y > 0, x − 3 < y < x + 3 (a) Find E(XY). (b) Find the covariance between X and Y.

1. The random variable X has probability density function: f(x) = ( ke−x 0 ≤ x...

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.

Consider a continuous random variable X with the probability density function f X ( x )...

Consider a continuous random variable X with the probability density function f X ( x ) = x/C , 3 ≤ x ≤ 7, zero elsewhere. Consider Y = g( X ) = 100/(x^2+1). Use cdf approach to find the cdf of Y, FY(y). Hint: F Y ( y ) = P( Y <y ) = P( g( X ) <y ) =

Assume that a continuous random variable has a following probability density function: f ( x )...

Assume that a continuous random variable has a following probability density function: f ( x ) = { 1 10 x 4 2 ≤ x ≤ 2.414 0 o t h e r w i s e Use this information and answer questions 3a to 3g. Question a: Which of the following is a valid cumulative density function for the defined region ( 2 ≤ x ≤ 2.414)? A.F x ( x ) = 1 50 x 5 −...

Subjects