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

MCQ

A random variable $X$ has the following probability distribution:

$X$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
$P(X)$	$0$	$K$	$2K$	$2K$	$3K$	$K^2$	$2K^2$	$7K^{2 }+ K$

Determine:

A
$K.$
B
$P(X < 3).$
C
$P(X > 6).$
✓
$P(0 < X < 3).$

✓

Answer

Correct option: D.

$P(0 < X < 3).$

Here $k + 2k + 2k + 3k + k^2 + 2k^2 + 7k^2 + k =1 $
$\Rightarrow 10k^2 + 9k –1 = 0$
$\Rightarrow (10k – 1) (k + 1) = 0$
$\Rightarrow k = \frac{1}{10}$
$\therefore\text{ (i) k =}\frac{1}{10}$
$(ii) P(x < 3) = 0 + k + 2k = 3k = \frac{3}{10}$
$(iii) P(x > 6) = 7k^2 + k = \frac{7}{100}+\frac{1}{10}=\frac{17}{100}$
$(iv) P(0 < x < 3) = k + 2k = 3k = \frac{3}{10}$

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 "5 Marks Questions" from Probability→Probability — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $\tan^{-1}\Big(\frac{\text{x}^2-\text{y}^2}{\text{x}^2+\text{y}^2}\Big)=\text{a}$ prove that $\frac{\text{dx}}{\text{dx}}=\frac{\text{y}}{\text{x}}\frac{(1-\tan\text{a})}{(1+\tan\text{a})}$

Solve the following differential equation:
$\text{x dy}=(2\text{y}+2\text{x}^4+\text{x}^2)\text{dx}$

Differentiate $\cos^{-1}(4\text{x}^3-3\text{x})$ with respect to $\tan^{-1}\Big(\frac{\sqrt{1-\text{x}^2}}{\text{x}}\Big),$ if $\frac{1}{2}<\text{x}<1$

$\text{If A} = \begin{bmatrix} 0 & 6 & 7 \\ -6 & 0 & 8 \\ 7 & -8 & 0 \end{bmatrix}, \text{B} = \begin{bmatrix} 0 & 1 & 1 \\ 1 & 0 & 2 \\ 1 & 2 & 0 \end{bmatrix}, \text{C} = \begin{bmatrix} 2 \\ -2 \\ 3 \end{bmatrix},$ then calculate AC, BC and (A + B) C. Also verify that (A + B) C = AC + BC.

Kellogg is a new cereal formed of a mixture of bran and rice that contains at least 88 grams of protein and at least 36 milligrams of iron. Knowing that bran contains 80 grams of protein and 40 milligrams of iron per kilogram, and that rice contains 100 grams of protein and 30 milligrams of iron per kilogram, find the minimum cost of producing this new cereal if bran costs Rs. 5 per kg and rice costs Rs 4 per kg.

find the area of the region bounded by y = |x - 1| and y = 1.

Find the vector equation of the line passing through the point (1, -1, 2) and perpendicular to the plane 2x - y + 3z - 5 = 0.

$\text{Evaluate:} \int\limits_0^\frac{\pi}{2} (2\log \sin \text{x} - \log \sin 2\text{x}) \text{dx}$

Evaluate the following intregals:
$\int\frac{2\text{x}+1}{\sqrt{\text{x}^2+2\text{x}-1}}\ \text{dx}$

Prove that:
$\cos^{-1}\frac{4}{5}+\cos^{-1}\frac{12}{13}=\cos^{-1}\frac{33}{65}$