6. The probability density function of (lifetime of an electronic component in years) X is f, (x)...
2) The lifetime in years of a certain type of electronic component has a probability density function given by: otherwise a) If the expected value of the random variable is 3/5 i.e. E(X)-3/5, find a and b. b) Show that the median lifetime is approximately 0.6501 years.
S 3x2/8 if 0 < x < 2 f(x) = { 0 otherwise is a probability density function. (a) What is F(x), the associated cdf? (6) What is F-1(x)? et U ~ . Use a random number generator to generate ten observations of U. (d) If X is a random variable with pdf f, use your answer to (c) to generate ten observations of X.
P7 continuous random variable X has the probability density function fx(x) = 2/9 if P.5 The absolutely continuous random 0<r<3 and 0 elsewhere). Let (1 - if 0<x< 1, g(x) = (- 1)3 if 1<x<3, elsewhere. Calculate the pdf of Y = 9(X). P. 6 The absolutely continuous random variables X and Y have the joint probability density function fx.ya, y) = 1/(x?y?) if x > 1,y > 1 (and 0 elsewhere). Calculate the joint pdf of U = XY...
3.22 The probability density function of a random variable X is shown below. fx(x) 0.4 (a) Find the constant A. Write a mathematical expression for the PDF. (b) Find the CDF for the case: 0 SXSA.
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given by f(x) - 3x2; 0< x < 1, - 0; otherwise Find the cumulative distribution function (i.e., cdf) of Y = X3 first and then use it to find the pdf of Y, E(Y) and V(Y)
For a continuous random variable X with the following probability density function (PDF): fX(x) = ( 0.25 if 0 ≤ x ≤ 4, 0 otherwise. (a) Sketch-out the function and confirm it’s a valid PDF. (5 points) (b) Find the CDF of X and sketch it out. (5 points) (c) Find P [ 0.5 < X ≤ 1.5 ]. (5 points)
is a continuous random variable with the probability density function (x) = { 4x 0 <= x <= 1/2 { -4x + 4 1/2 <= x <= 1 What is the equation for the corresponding cumulative density function (cdf) C(x)? [Hint: Recall that CDF is defined as C(x) = P(X<=x).] We were unable to transcribe this imageWe were unable to transcribe this imageProblem 2. (1 point) X is a continuous random variable with the probability density function -4x+41/2sxs1 What is...
For the probability density function f defined on the random variable x, find (a) the mean of x, (b) the standard deviation of x, and (c) the probability that the random variable x is within one standard deviation of the mean. f(x) = 1 30 x, [2,8] a) Find the mean. u = (Round to three decimal places as needed.) b) Find the standard deviation. = (Round to three decimal places as needed.) c) Find the probability that the random...
Q1) A-Random variable X has the following Probability Density Function (PDF) fr(x)= 부.lel s 3. (0, xl>3, A1-Show that fr (x) is a valid PDF. B- X is a uniform (-1,3) random variable. Let Y be the output of a clipping circuit with the input X such that Y - 80Q) where χ>0. , B1-Find P(Y-1). B2-Find P(Y 3). B3-Derive and plot the cumulative distribution function (CDF) of the random variable Y, Fy (). B4-What is the probability density function...
6. Here is the graph of the probability density function (pdf) fx for a continuous random variable X 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 6 10 (a) Sketch the cumulative distribution function (cdf) of X. Label the vertical axis appropriately. (b) Which is larger, P(X 2) or P(X 6)? Explain how you know c) Which is larger, P(1.999 X 2.001) or P(5.999 s X .00)? Explain how you know (d) Which is larger, P(1s X S3) or P(5...