[عاشقة المساء]

Q-5 An urn contains 10 marbles, each of which shows a number. Five marbles show 1,two marbles show 2 and three show 3.
A marble is drawn at random. If x is the number that shows find the followings:

The probability distribution and the cumulative distribution of the random variable x.
p(1≤x≤3),p(x<3) .
Find the mean of the random variable X.
Calculate the variance and standard deviation of the random variable X.



Q-6:The density function for a random variable X is given by

f(x)={(_0 , otherwise^(1/2 x, if 0≤x≤2)) ┤
Find the cumulative distribution function.
Find p(1/2<x<1)
Find p(x<1)
Find the mean of the random variable x.
Find the standard deviation of the random variable x.