The random variable X has density functionwhere k is a constant. What is the median of X?
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The random variable X has density function F(x)= (k+1)x^2 for 0<x<1 and 0 otherwise, where k is a constant. What is the median of X?
The random variable X has density function F(x)= (k+1)x^2 for 0<x<1 and 0 otherwise, where k is a constant. What is the median of X?
1. Let the random variable X have the density function k for 0 f (ar) 0 elsewhere. If the mode of this distribution is at x =-42, then what is the median of X?
The random variable X has probability density function k(x25x-4) 1<x<4 otherwise -{ f(x) 1. Show thatk. (5pts) Find 2. Е (X), (5pts) 3. the mode of X, (5pts) 4. the cumulative distribution function F(X) for all x. (5pts) 5. Evaluate P(X < 2.5). (5pts) 6. Deduce the value of the median and comment on the shape of the distribution (10pts)
Suppose the random variable X has probability density function (pdf) - { -1 < x<1 otherwise C fx (x) C0 : where c is a constant. (a) Show that c = 1/7; (b) Graph fx (х); (c) Given that all of the moments exist, why are all the odd moments of X zero? (d) What is the median of the distribution of X? (e) Find E (X2) and hence var X; (f) Let X1, fx (x) What is the limiting...
The random variable X has probability density function f (x) = k(−x²+5x−4) 1 ≤ x ≤ 4 or =0 1 Show that k = 2/9 Find 2 E(X), 3 the mode of X, 4 the cumulative distribution function F(X) for all x. 5 Evaluate P(X ≤ 2.5). 6 Deduce the value of the median and comment on the shape of the distribution.
EXERCISE (x2+1), where . < 1) A random variable X has the density function f(x)= a) Find the value of the constant C b) Find the probability that X lies between 1/3 and 1
2. The random variable X has probability density function f given by f(x) 0 otherwise. (a) Is X continuous or discrete? Explain. (b) Calculate E(X). (c) Calculate Var(2X 9).
A continuous random variable X has the density 3 x for f(x) = 0 otherwise. What is the probability that X is greater than its 75th percentile?
19. A random variable X has the pdf f(x) = 2/3 0 otherwise if 1 < x 2 (a) Find the median of X. (b) Sketch the graph of the CDF and show the position of the median on the graph.
4. The random variable X has probability density function f(x) given by f(x) = { k(2- T L k(2 - x) if 0 sxs 2 0 otherwise Determine i. the value of k. ii. P(0.7 sX s 1.2) iii. the 90th percentile of X.