The random variable X has probability density function f (x) = k(−x²+5x−4) 1 ≤ x ≤...
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.
Homework Answers
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The random variable X has probability density function
f (x) = k(−x²+5x−4) 1 ≤ x ≤...
The random variable X has probability density function k(x25x-4) 1<x<4 otherwise -{ f(x) 1. Show thatk....
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)
Let X be the random variable whose probability density function is f(x) = ce−5x , if...
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6. Let X be a continuous random variable whose probability density function is: 0, x <0,...
6. Let X be a continuous random variable whose probability density function is: 0, x <0, x20.5 Find the median un the mode. 7. Let X be a continuous random variable whose cumulative distribution function is: F(x) = 0.1x, ja 0S$s10, Find 1) the densitv function of random variable U-12-X. 0, ja x<0, I, ja x>10.
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2x 0<x<1 Let X be a continuous random variable with probability density function f(x)= To else...
2x 0<x<1 Let X be a continuous random variable with probability density function f(x)= To else The cumulative distribution function is F(x). Find EX.
The random variable X has probability density function k(x25x-4) 1<x<4 otherwise -{ f(x) 1. Show thatk. (5pts) Find 2. Е (X), (5pts) 3. the mode of X, (5pts) 4. the cumulative distribution function F(X) for all x. (5pts) 5. Evaluate P(X < 2.5). (5pts) 6. Deduce the value of the median and comment on the shape of the distribution (10pts)
6. Let X be a continuous random variable whose probability density function is: 0, x <0, x20.5 Find the median un the mode. 7. Let X be a continuous random variable whose cumulative distribution function is: F(x) = 0.1x, ja 0S$s10, Find 1) the densitv function of random variable U-12-X. 0, ja x<0, I, ja x>10.
Show that the function f(x)=1/(x^2+π^2 ) can be taken as a
probability density (distibution) function of a random variable X.
Find p(X>π). Find also the cumulative distribution function F(x)
of the random variable X. Find, finally, mean and standard
deviation of the random variable X
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