Download App

APPLICATION OF DERIVATIVES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAPPLICATION OF DERIVATIVES5 Marks
Question
Three numbers are selected at random (without replacement) from first six positive integers. If X denotes the smallest of the three numbers obtained, find the probability distribution of X. Also find the mean and variance of the distribution.
✓

Answer

Total number of ways $^6\text{C}_3=20$
$\text{X:}$ 1 2 3 4
$\text{P(X):}$ $\frac{10}{20}$ $\frac{6}{20}$ $\frac{3}{20}$ $\frac{1}{20}$
$\text{XP(X):}$ $\frac{10}{20}$ $\frac{12}{20}$ $\frac{9}{20}$ $\frac{4}{20}$
$\text{X}^{2}\text{P(X)}:$ $\frac{10}{20}$ $\frac{24}{20}$ $\frac{27}{20}$ $\frac{16}{20}$
$\text{Mean} = \sum \text{XP(X)} =\frac{35}{20} = \frac{7}{4}$
$\text{Variance} = \sum \text{X}^{2}\text{P(X)} - \bigg[\sum\text{XP(X)}\bigg]^{2}= \frac{77}{20} - \frac{49}{16} = \frac{63}{80}$

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 APPLICATION OF DERIVATIVES→APPLICATION OF DERIVATIVES — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Two dice are drawn together and the number appearing on them noted. X denotes the sum of the two numbers. Assuming that the 36 outcomes are equally likely, what is the probability distribution of X?
→
Draw a rough sketch of the region $\{(x, y) : y^2 < 3x, 3x^2 + < 16\}$ and find the area by the region using mwthod of integration.
→
In a certain college, $4\%$ of boys and $1\%$ of girls are taller than $1.75$ metres. Further more, $60\%$ of the students in the colleges are girls. A student selected at random from the college is found to be taller than $1.75$ metres. Find the probability that the selected students is girl.
→
Find the matrix X satisfying the equation:$\begin{bmatrix}2 & 1 \\5 & 3 \end{bmatrix}\text{X}\begin{bmatrix}5 & 3 \\3 & 2 \end{bmatrix}=\begin{bmatrix}1 & 0 \\0 & 1 \end{bmatrix}.$
→
Evaluate the following integrals:
$\int\frac{\text{x}^2}{(\text{x}^2+1)(3\text{x}^2+4)}\ \text{dx}$
→
Find the area of the bounded by $\text{y}=\sqrt{\text{x}}$ and $y^2 = x$.
→
Evaluate the following intregals:
$\int\frac{\text{x}}{(\text{x}+1)(\text{x}^2+1)}\ \text{dx}$
→
Using direction ratios show that the points A(2, 3, -4) B(1, - 2, 3) and C(3, 8, -11) are collinear.
→
Find the equation of the plane passing through the line of intersection of the planes $2x - 7y + 4z = 0, 3x - 5y + 4z + 11 = 0$ and the point $(-2, 1, 3).$
→
If $\text{x}\sin(\text{a}+\text{y})+\sin\text{a}\cos(\text{a}+\text{y})=0,$ prove that $\frac{\text{dy}}{\text{dx}}=\frac{\sin^2(\text{a}+\text{y})}{\sin\text{a}}$
→