2.5.9. The random variable X has a cumulative distribution function for xo , for xsO ....
2.5.9. The random variable X has a cumulative distribution function for xo , for xsO . for r>0 F(x) = z? 1 +x2 Find the probability density function of X.
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2.5.9. The random variable X has a cumulative distribution function 0, forx<0 F(x) for x > 0. for x > , 1+x2" · Find the probability density function of X.
Q2. Assume that X is a continuous and nonnegative random variable with the cumulative distribution function Fx Let b> 0. (a) Find the cumulative distribution function of Y = XI(X < b} (b) Apply the general formula from (a) to exponential distribution with parameter λ > 0.
Measurement of a blood test is a random variable X with cumulative distribution function given by 0, 1, r >2 a. Find fx(x), the probability density function b. Graph fx(x) c. Find the mean and the variance of X d. Find the median of X
Q1. Assume that X is a continuous and nonnegative random variable with the cumulative distribution function F and density f. Let b>0. (a) Write the forinula for E(X b)+1. (b) Apply the general formula from (a) to exponential distribution with parameter λ > 0.
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Determine values of the cumulative distribution function for the random variable in the previous problem. 3. 2. The probability mass function below is defined for x 0, 1,2,3,.. fr 5 5 -56 What is the probability for each of the following expressions? a) P(X 2) b) P(XE 2) c) P(X> 2) d) P(X2 1)
Let X be a continuous random variable with the following density function. Find E(X) and var(X). 6e -7x for x>0 f(x) = { for xso 6 E(X) = 49 var(X) =
Problem 9: 10 points Suppose that X, Y are two independent identically distributed random variables with the density function f(x)= λ exp (-Az), for >0. Consider T- and find its cumulative distribution function and density function.
Q2. Assume that X is a continuous and nonnegative random variable with the cumulative distribution function Fx. Let b > 0 a) Find the cumulative distribution function ofY -XKX< (b) Apply the general formula fron (a) to exponential distribution with parameter > 0.
Q3. Assume that X is a continuous and nonnegative random variable with the cumulative distribution function Fx Let b>0 (a) Find the cumulative distribution function of Y- (X -b)+ (b) Apply the general formula from (a) to Pareto distribution with parameter a > 0. Hint: Consider separately cases b e (0, 1] and b> 1.