The probability distribution function oif a random variable X is … - Vidyadip

Question

The probability distribution function oif a random variable $X$ is given by

$X_i$	$0$	$1$	$2$
$P_i$	$3c^3$	$4c - 10c^2$	$5c - 1$

Where $c > 0$
Find: $\text{P}(1<\text{X}\leq2)$

✓

Answer

$\text{P}(1<\text{X}\leq2)$
$=\text{P}(\text{X}=2)$
$=5\text{c}-1$
$=\frac{5}{3}-1$
$=\frac{5-3}{3}$
$=\frac{2}{3}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Mean and variance of a random variable→Mean and variance of a random variable — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $\text{f(x)}=\begin{cases}\frac{1-\cos\text{x}}{\text{x}^2},&\text{x}\neq0\\\text{k},&\text{x}=0\end{cases}$ is continuous at x = 0, find k.

If $x\begin{bmatrix}2\\3\end{bmatrix} +y\begin{bmatrix}-1\\1\end{bmatrix} = \begin{bmatrix}10\\5\end{bmatrix}, $find the values of x and y.

The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs.
at least one will fuse after 150 days of use.

Integrate the function: $\sqrt{\sin 2 x} \cos 2 x$

Write the function in the simplest form: $\tan ^{-1}\left(\frac{\cos x-\sin x}{\cos x+\sin x}\right),-\frac{\pi}{4}<x<\frac{3\pi}{4}$

If $\text{A}=\begin{bmatrix} 1 & -3 \\ 2 & 0 \end{bmatrix},$ write adj $A.$

Evaluate the following integrals:$\int\frac{\text{e}^\text{x}}{1+\text{e}^{2\text{x}}}\text{dx}$

If u, v and w are functions of x, then show that
$\frac{d}{d x}(u . v . w)=\frac{d u}{d x} v . w+u . \frac{d v}{d x} \cdot w+u \cdot v \frac{d w}{d x}$
in two ways - first by repeated application of product rule, second by logarithmic differentiation.

If $\vec{\text{a}}.\vec{\text{a}}=0$ and $\vec{\text{a}}.\vec{\text{b}}=0,$ what can you conclude about the vector $\vec{\text{b}}$?

Show that $\left[\begin{array}{ccc} {1} & {2} & {3} \\ {0} & {1} & {0} \\ {1} & {1} & {0} \end{array}\right]\left[\begin{array}{rrr} {-1} & {1} & {0} \\ {0} & {-1} & {1} \\ {2} & {3} & {4} \end{array}\right] \neq\left[\begin{array}{rrr} {-1} & {1} & {0} \\ {0} & {-1} & {1} \\ {2} & {3} & {4} \end{array}\right]\left[\begin{array}{lll} {1} & {2} & {3} \\ {0} & {1} & {0} \\ {1} & {1} & {0} \end{array}\right]$