If the probability distribution of a random variable X is given b… - Vidyadip

Question

If the probability distribution of a random variable X is given below:

X = X_i	1	2	3	4
P(X = X_i)	c	2c	4c	4c

Write the value of $\text{P}(\text{X}\leq2)$

✓

Answer

We know that the sum of probabilities in a probability distribution is always 1.
Therefore,
P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 1
⇒ c + 2c + 4c + 4c =1
⇒ 11c = 1
$\Rightarrow\text{c}=\frac{1}{11}$
Now,
$\text{P}(\text{X}\leq2)=\text{P}(\text{X}=1)+\text{P}(\text{X})=2=\frac{1}{10}+\frac{2}{10}=\frac{3}{10}$

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" from Mean and variance of a random variable→Mean and variance of a random variable — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Evaluate $\begin{vmatrix}\cos\alpha\cos\beta&\cos\alpha\sin\beta&-\sin\alpha\\-\sin\beta&\cos\beta&0\\\sin\alpha\cos\beta&\sin\alpha\sin\beta&\cos\alpha\end{vmatrix}.$

Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\frac{\text{d}^3\text{x}}{\text{dt}^3}+\frac{\text{d}^3\text{x}}{\text{dt}^2}+\Big(\frac{\text{ dx}}{\text{dt}}\Big)^2=\text{e}^\text{t}$

Find the area bounded by the curve y = cos x between x = 0 and x = 2$\pi$

Construct a 2 × 2 matrix A = [a_ij] whose elements a_ij are given by:
$\text{a}_\text{ij}=\frac{(\text{i}-\text{j})^2}{2}$

If f is an integrable function, show that:
$\int\limits^{\text{a}}_{-\text{a}}\text{f}\big(\text{x}^2\big)\text{dx}=2\int\limits^\text{a}_0\text{f}\big(\text{x}^2\big)\text{dx}$

Write A^-1 for $\text{A}=\begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix}$

f: Z → Z given by f(x) = x³

If $\vec{\text{a}},\ \vec{\text{b}},\ \vec{\text{c}}$ are non-coplanar vectors, prove that the given vectors are non-coplanar:
$2\vec{\text{a}}-\vec{\text{b}}+3\vec{\text{c}},\ \vec{\text{a}}+\vec{\text{b}}-2\vec{\text{c}}$ and $\vec{\text{a}}+\vec{\text{b}}-3\vec{\text{c}}$

Find the unit vector along the sum of the vectors $\vec{a}=2 \hat{i}+2 \hat{j}-5 \hat{k}$ and $\vec{b}=2 \hat{i}+2 \hat{j}+\hat{k}$.

What is the cosine of the angle with the vector $\sqrt2\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}$ makes with y-axis?