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drawar
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Homework Statement
The continuous random variable X has cumulative distribution function given by
[tex]F(x) = \left\{ {\begin{array}{*{20}c}
0 & {x \le 0} \\
{\frac{{x^2 }}{k}} & {0 \le x \le 1} \\
{ - \frac{{x^2 }}{6} + x - \frac{1}{2}} & {1 \le x \le 3} \\
1 & {x \ge 3} \\
\end{array}} \right.[/tex]
(i) Find the value of k
(ii) Find the probability density function of X and sketch its graph
(iii) Find the median of [tex]\sqrt X[/tex]
(iv) 10 independent observations of X are taken. Find the probability that eight of them are less than 2.
(v) Let A be the event X > 1 and B be the event X > 2. Find P(B|A)
Homework Equations
The Attempt at a Solution
I'm able to do the first 2 questions
For (i), by substitution I get k=3
For (ii), I take the derivative of F(x), then [tex]f(x) = \left\{ {\begin{array}{*{20}c}
{\frac{{2x}}{3}} & {0 \le x \le 1} \\
{ - \frac{x}{3} + 1} & {1 \le x \le 3} \\
0 & {otherwise} \\
\end{array}} \right.[/tex]
However, I have no idea how to do the rest. Any feedback is appreciated, thanks
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