(50 points) For the probability density function shown below (a) Determine the expected value of X...
1. (50 points) For the probability density function shown below (a) Determine the expected value of X. (b) What is the probability that X is less than 2? (c) What is the probability that X is between 1 and 2? fx(x) _ 2 3 2. (50 points) Suppose that the diameter X of a certain type of weld is uniformly distributed between 0.2 mm and 4.2 mm. (a) Determine and plot the PDF and CDF of X. (b) What is...
1. The probabslity density function for x io given below. I y-x', determine the probability that y falls between 0.5 and 1.5. choose the closest answer fr (x) 0srs fx (x)-2-x 1srs2 a. 0.40 b. 0.41 c. 0.42 d. 0.43 e. 0.44 f. 0.45 g. 0.46 h. 0.47 i. 0.48 j. 0.49 k. 0.50 Answer_ 2. For the probability density function for X in problem 1, determine the 95% value of X. That is, the value of X such that...
2. Let X and Y be continuous random variables with joint probability density function fx,y(x,y) 0, otherwise (a) Compute the value of k that will make f(x, y) a legitimate joint probability density function. Use f(x.y) with that value of k as the joint probability density function of X, Y in parts (b),(c).(d),(e (b) Find the probability density functions of X and Y. (c) Find the expected values of X, Y and XY (d) Compute the covariance Cov(X,Y) of X...
Let X be a random variable with probability density function fx= c1-x2, -1<x<10, otherwise What is the support of X? What is the value of c? Sketch the probability density function of X. Find P(X<0). Find P(X<0.5). Find P(X<2). Determine the expected value of X.
7. A random process may be modeled as a random variable with the probability density function fx(x) fx(x) fx(x) x < 1/2 x 1 /2 = 2-4x = 4x-2 = 0 (a) Show that Jdfx(r)dr = 1 (b) Find the CDF, Fx() (c) Find the probability that X is between 1/3 and 2/3. (d) Find the expected value of X. (e) Find the mode of X (f) Find the median of X. (g) Find the variance of X and the...
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.
4. Two random variables X and Y have the following joint probability density function (PDF) Skx 0<x<y<1, fxy(x, y) = 10 otherwise. (a) [2 points) Determine the constant k. (b) (4 points) Find the marginal PDFs fx(2) and fy(y). Are X and Y independent? (c) [4 points) Find the expected values E[X] and EY). (d) [6 points) Find the variances Var[X] and Var[Y]. (e) [4 points) What is the covariance between X and Y?
3. (10 points) Let X be continuous random variable with probability density function: fx(x) = 7x2 for 1<<2 Compute the expectation and variance of X 4. (10 points) Let X be a discrete random variable uniformly distributed on the integers 1.... , n and Y on the integers 1,...,m. Where 0 < n S m are integers. Assume X and Y are independent. Compute the probability X-Y. Compute E[x-Y.
Random variable x has a uniform distribution defined by the probability density function below. Determine the probability that x has a value of at least 220. f(x) = 1/100 for values of x between 200 and 300, and 0 everywhere else a)0.65 b)0.80 c)0.75 d)0.60
Consider fx (x)=e*, 0<x and joint probability density function fx (x, y) = e) for 0<x<y. Determine the following: (a) Conditional probability distribution of Y given X =1. (b) ECY X = 1) = (c) P(Y <2 X = 1) = (d) Conditional probability distribution of X given Y = 4.