3,40 A random variable X has probability density function fx(x) = 1 0<x< 1. Find the...
2.5.6. The probability density function of a random variable X is given by f(x) 0, otherwise. (a) Find c (b) Find the distribution function Fx) (c) Compute P(l <X<3)
A probability distribution function for a random variable X has the form Fx(x) = A{1 - exp[-(x - 1)]}, 1<x< 10, -00<x<1 (a) For what value of A is this a valid probability distribution function? (b) Find the probability density function and sketch it. (c) Use the density function to find the probability that the random variable is in the range 2 < X <3. Check your answer using the distribution function. (d) Find the probability that the random variable...
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.
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]
1. A continuous random variable has probability density function f(x) = 2x for all 0 < x < 1 and f(x) = 0 for all other 2. Find Prli <x< 1. O 1 16 O OP O . O 1
A mixed random variable X has the cumulative distribution function e+1 (a) Find the probability density function. (b) Find P(0< X < 1).
[Total Marks: 301 ={} Question 1 A random variable X has a probability density function as defined below. (x + 1 -1<x<0 fx(x) = (-x+1 0<x< 1 Find the following: a) The cumulative distribution function of X, Fx(x). b) P(x > 0.1 X < 0.5). c) The conditional probability density function fx(x = 0.6 X > 0.5). [10 Marks [5 Marks [15 Marks]
2x 0<x<1 Let X be a continuous random variable with probability density function f(x)= To else The cumulative distribution function is F(x). Find EX.
Random variables X and Y have the following joint probability density function, fx,y(x, y) = {c)[4] < 15.36, 1y| < 15.367 1.36} 0, 0.w. where cis a constant. Calculate P(Y – X| < 8.41).
4. Let X be a continuous random variable with probability density function: x<1 0, if if| if x>4 f(x) = (x2 + 1), 4 x 24 0 Find the standard deviation of random variable X.