Let X Be a Continuous Random Variable With Pdf FXlambdaAlphaxalpha
Question
Probability
1.Let X be a continuous random variable with the probability density function
f(x)=k \cdot \sqrt{x}, \quad 0 \leq x \leq 4
\begin{aligned} & f(x)=0, \\ & \text{^^20otherwise.^^20}\end{aligned}
a)What must the value of k be so that f(x) is a probability density function?
b)Find the cumulative distribution function of X, Fx(x)=P(X<=x).
c)Find the probability P(1<= X <=2).
d)Find the median of the distribution of X. That is, find m such that P(X<=m)=P(X >=m) =½.
e) Find the 30th percentile of the distribution of X.
\text { f) Find } \mu_{X}=E(X) \text { . }
\text { g) Find } \sigma_{X}=\operatorname{SD}(X) \text { . }
Answer
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