Problem 1) The area under a probability density function is equal to a) 100 b) 10...
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...
(d) Find the probability mass function of X given Y = 3 (ie, p(x|y = 3)) 7. (10 points) Consider two jars, Jar M and Jar W. In Jar M, there are 3 balls numbered 0, 1, 2. In Jar W there are 3 balls numbered 1, 2, 3. A ball is drawn from Jar M, then a ball is drawn from Jar W. Define M as the number on the ball from Jar A and W the number on...
1. Suppose the random variable X has the following probability density function: Problem Set: 1. Suppose the random variable X has the following probability density function: p(x) = fcx 0sxs2 10 otherwise. ] Note this probability density function is also of the form of an unknown parameter c. (a) Determine the value of c that makes this a valid probability density function. (b) Determine the expected value of X, E[X]. (c) Determine the variance of X, V(X).
the joint probability density function is given by 1. The joint probability density function (pdf) of X and Y is given by fxy(x,y) = A (1 – xey, 0<x<1,0 < y < 0 (a) Find the constant A. (b) Find the marginal pdfs of X and Y. (c) Find E(X) and E(Y). (d) Find E(XY).
(a)The continuous random variable X is distributed with probability density function f defined by f(x) = (1/64)x * (16 - x^2) , for 0 < x < 4. . Find [V (2x+1)] . (b) -An urn contains 7 white balls and 3 black balls. Two balls are selected at random without replacement. What is the probability that: 1-The first ball is black and the second ball is white. 2-One ball is white and the other is black ( C)- Suppose...
Please help me with this problem 1 point) The following density function describes a random variable X. A. Find the probability that X lies between 2 and 4. Probability: B. Find the probability that X is less than 3. Probability:
Problem 3. The probability density function of X is f(x)o otherwise where k is some positive number. (a) Determine the value of the constant k. (b) Find the distribution function F(x)- P(X S r). (c) Compute μ-E(X), the mean of X. (d) Compute σ2-Var(X), the variance of X.
Consider a continuous random variable X with the following probability density function: Problem 2 (15 minutes) Consider a continuous random variable X with the following probability density function: f(x) = {& Otherwise ?' 10 otherwise? a. Is /(x) a well defined probability density function? b. What is the mathematical expectation of U (2) = x (the mean of X, )? c. What is the mathematical expectation of U(z) = (1 - 2 (the variance of X, oº)?
We were unable to transcribe this imagefunction givě by: . When measured at a location, has a probability density fy(y) 0, elsewhere a) Find the value of k that makes fy(y) a density function. Hint: Does the density have the form of a "known" distribution? b) Determine the mean of Y, E(Y). Hint: a previous problem may be very helpful! c) Using R, simulate 100 values from this distribution and determine the mean of these 100 values. How close is...
2. A random variable has a probability density function given by: Bmx-(B+1) x20 x<m fx(x)= 10 where m>0 and B > 2. Let m and ß be constants; answer the questions in terms of m and B. (a) Find the cumulative distribution function (cdf) Fx(x) of this random variable; (b) Find the mean of X; (c) Find E[X']; and (d) Find the variance of X. [12 points]