5. X has a normal density: f(x) = atze-(+) Show that P(X - Hl> ko) is...
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a random variable X has density function f(x) = cx2 for 0<x<3 and f(x) = 0 others. a. Find constant value o b. Find probability P(1 < X<2
2. The random variable X has density ke-lal. Find P(|X| + |X – 31 < 5). A. .716 B. .235 C. .807 D. .344
X is a random variable with density function f(x) = x² /3 for -1 < x < 2,0 else. U is uniform(0,1). Find a function g such that g(U) has the same distribution as X.
1. Let X be a continuous random variable with probability density function f(x) = { if x > 2 otherwise 0 Check that f(-x) is indeed a probability density function. Find P(X > 5) and E[X]. 2. Let X be a continuous random variable with probability density function f(x) = = { SE otherwise where c is a constant. Find c, and E[X].
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a random variable X has density function f(x) = cx2 for 0<x<3 and f(x)= 0 others. a. Find constant value o b. Find probability P(1 < X < 2)
Suppose that the standard normal random variables X and Y are independent. Find P(0 < X<Y). 8 O 1 4T 0 1 8л Ala
1. If f(x) is a Density Function, what is the value of k? Skr3, 0<x<1, f(0) 0, elsewhere.
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)
. A random variable X with P(X> 0) 1 has density function f(x) cx299e3. Find: with P(X >0) 1 has density function f (x)cx2s e ) E(X) ) Var(x)
A random variable, x, has a normal distribution with u = 15.9 and o = 2.80. Determine a value, Xo, 50 that: a. P(x>xo) -0.05 Хо (Round to one decimal place as needed.) b. Plxsxo) = 0.975 Хо (Round to one decimal place as needed.)