A random variable X has the following probability distribution: X… - Vidyadip

MCQ

A random variable X has the following probability distribution:

$X = x$	1	2	3	4
P$(X = x)$	k	2k	3k	4k

The value of $\mathrm{P}(\mathrm{X}<3)$ is

A
0.1
B
0.2
✓
0.3
D
0.4

✓

Answer

Correct option: C.

0.3

(C)
Since $\sum_{x=1}^4 \mathrm{P}(\mathrm{X}=x)=1$,
$\begin{aligned}& \mathrm{k}+2 \mathrm{k}+3 \mathrm{k}+4 \mathrm{k}=1 \\& \Rightarrow 10 \mathrm{k}=1 \\& \Rightarrow \mathrm{k}=\frac{1}{10}\end{aligned}$
Now, $\mathrm{P}(\mathrm{X}<3)=\mathrm{P}(\mathrm{X}=1)+\mathrm{P}(\mathrm{X}=2)$
$\begin{aligned} & =\mathrm{k}+2 \mathrm{k} \\ & =3 \mathrm{k}=3\left(\frac{1}{10}\right)=0.3\end{aligned}$

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 "MCQ" from Probability Distributions→Probability Distributions — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Let $f : R - {n} \rightarrow R$ be a function defined by $\text{f(x)}=\frac{\text{x}-\text{m}}{\text{x}-\text{n}},$ where $\text{m}\neq\text{n.}$ Then,

$\int_0^{\pi / 2} \frac{\sin ^{\frac{3}{2}} x d x}{\cos ^{\frac{3}{2}} x+\sin ^{\frac{3}{2}} x}=$

The line joining origin and point of intersection of curves $a x^2+2 h x y$$+ b y^2+$$2 g x=0$ and $a _1 x ^2+2 h_1 x y+ b _1 y^2+2 g_1 x=0$ will be mutually perpendicular if

If the volume of the parallelopiped with coterminous edges $-p \hat{j}+5 \hat{k}, \hat{i}-\hat{j}+q \hat{k}$ and $3 \hat{i}-5 \hat{j}$ is 8 , then

The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probablity of 2 successes is

$\int \frac{\sin 4 x}{\sin x} d x=$ (Where $C$ is a constant of integration.)

If $f(x)=3 x^3-9 x^2-27 x+15,$ then the maximum value of $f(x)$ is

If $m_1, m_2$ are slopes of lines represented by $2 x^2-5 x y+3 y^2=0$ then equation of lines passing through origin with slopes $\frac{1}{m_1}, \frac{1}{m_2}$ will be

If $x=\sqrt{e^{\sin ^{-1} t}}$ and $y=\sqrt{e^{\cos ^{-1} t}}$, then $\frac{d^2 y}{d x^2}$ is

The direction ratios of the line $x - y + z - 5 = 0 = x - 3y - 6$ are proportional to: