A discrete random variable X has the probability distribution giv… - Vidyadip

Question

A discrete random variable X has the probability distribution given below:

X:	0.5	1	1.5	2
P(X):	k	$k^2$	$2k^2$	k

Find the value of k.

✓

Answer

We know that,
$P(0.5) + P(1) + P(1.5) + P(2) = 1$
$k + k^2+ 2k^2 + k = 1$
$3k^2 + 2k - 1 = 0$
$3k^2 + 3k - k - 1 = 0$
$(3k - 1)(k + 1) = 0$
$\text{k}=\frac{1}{3}$ or $\text{k}=-1$
We know that $0\leq\text{P}(\text{X})\leq1$
$\therefore\ \text{k}=\frac{1}{3}$

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→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Write $\cot^{-1}$ $\left(\frac{1}{\sqrt{x^{2}-1}}\right), x>1$ in the simplest form.

A discrete random variable X has the probability distribution given below:

X:	0.5	1	1.5	2
P(X):	$k$	$k^2$	$2k^2$	$k$

Determine the mean of the distribution.

Find the domain of $\text{f(x)}=\cos^{-1}\text{x}=\cos\text{x}$

If $f: R → R$ is defined by $f(x) = x^2 – 3x + 2,$ find $f(f(x)).$

A die is tossed thrice. Find the probability of getting an odd number at least once.

Evaluate the following:
$\cot^{-1}\Big(\cot\frac{19\pi}{6}\Big)$

Evaluate the definite integral in Exercise:$\int\limits_{0}^{\frac{\pi}{2}}\cos2\text{x}\ \text{dx}$

The total cost $C(x)$ associated with the production of $x$ units of an item is given by $C(x) = 0.005x^3 – 0.02x^2 + 30x + 5000.$ Find the marginal cost when $3$ units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.

Construct a $2 \times 3$ matrix $A = [a_{ij}]$ whose elements $a_{ij}$ are give by:
$a_{ij} = i.j$

Find the slope of the tangent to the curve $\text{y} = \frac{\text{x}-1}{\text{x}-2},\ \text{x} \neq \text{at}\ \text{x} = 10.$