Download App

Probability Distributions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsProbability Distributions2 Marks
MCQ
X is a continuous random variable with probability density function
$f(x)=\left\{\begin{array}{cc}\frac{x}{6}+k ; & 0 \leq x \leq 3 \\0 ; & \text { otherwise }\end{array}\right.$
The value of k is equal to
  • ✓
    $\frac{1}{12}$
  • B
    $\frac{1}{3}$
  • C
    $\frac{1}{4}$
  • D
    $\frac{1}{6}$
✓

Answer

Correct option: A.
$\frac{1}{12}$
(A)
Since, $\mathrm{f}(x)$ is the p.d.f. of X .
$\therefore \quad \int_{-\infty}^{\infty} \mathrm{f}(x) \mathrm{d} x=1$
$\begin{aligned} & \Rightarrow \int_0^3\left(\frac{x}{6}+\mathrm{k}\right) \mathrm{d} x=1 \\ & \Rightarrow\left[\frac{x^2}{12}+\mathrm{k} x\right]_0^3=1 \Rightarrow \frac{3}{4}+3 \mathrm{k}=1 \\ & \Rightarrow 3 \mathrm{k}=\frac{1}{4} \Rightarrow \mathrm{k}=\frac{1}{12}\end{aligned}$

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

The area (in sq. units) of the region bounded by the X-axis and the curve $y=1-x-6 x^2$ is
→
The function $\text{f(x)}=|\cos\text{x}|$ is:
→
Which of the following distribution of probabilities of a random variable X is the probability distribution?
→
If $A=\left[\begin{array}{ccc}1 & 0 & 0 \\ 3 & 3 & 0 \\ 5 & 2 & -1\end{array}\right]$, then $\operatorname{adj} A$ is
→
If $A$ and $B$ are invertible matrices, which of the following statement is not correct.
→
The area bounded by the circle $x^2+y^2=4$, line $x=\sqrt{3} y$ and $X$-axis lying in the first quadrant, is
→
Let $\begin{vmatrix}\text{x}^2+3\text{x}&\text{x}-1&\text{x}+ 3\\\text{x}+1&-2\text{x}&\text{x}-4\\\text{x}-3&\text{x}+4&3\text{x}\end{vmatrix}=\text{ax}^4+\text{bx}^3+\text{cx}^2+\text{dx}+\text{e}$ be an identity in $x,$ where $a, b, c, d, e$ are independent of $x.$ Then the value of $e$ is:
→
If $|\overline{ a }|=1$, then $\overline{ a }$ is a
→
The area of the region bounded by the ellipse $x^2 / 64+y^2 / 100=1$, is ____ sq.units
→
The separate equations of the lines represented by the equation $a x^2+( a + b ) x y+ b y^2+x+y=0$ are
→