A continuous random variable \(X\) has probability density function \(f(x)\) given by \(f(x)=\left\{\begin{array}{cl} 12 x^2(1-x), & \text { for } 0 \leq x \leq 1 \\ 0, & \text { for all other values of } x \end{array}\right.\) --- 6 WORK AREA LINES (style=lined) --- --- 6 WORK AREA LINES (style=lined) --- --- 5 WORK AREA LINES (style=lined) ---
Statistics, 2ADV S3 SM-Bank 20
A continuous random variable `X` has a probability density function given by
`f(x) = {{:(Cx + D),(0):}\ \ \ \ {:(2 <= x <= 5),(text(elsewhere)):}:}`
where `C` and `D` are constants.
Find the exact values of `C` and `D`, given the median of `X` is 4. (4 marks)
--- 8 WORK AREA LINES (style=lined) ---
Statistics, 2ADV S3 SM-Bank 10
A continuous random variable, `X`, has a probability density function given by
`f(x) = {{:(1/5e^(−x/5),x >= 0),(0, x < 0):}`
The median of `X` is `m`.
Determine the value of `m`. (3 marks)
Statistics, 2ADV S3 SM-Bank 7 MC
A probability density function `f(x)` is given by
`f(x) = {(1/12 (8x -x^3)), (\ 0):} qquad {:(0 <= x <= 2), (text(elsewhere)):}`
The median `m` of this function satisfies the equation
A. `-m^4 + 16m^2 - 6 = 0`
B. `m^4 - 16m^2 = 0`
C. `m^4 - 16m^2 + 24 = 0.5`
D. `m^4 - 16m^2 + 24 = 0`