Download App

13. probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths13. probability1 Mark
MCQ
A random variable $X$ has Poisson’s distribution with mean $2$. Then $P(X > 1.5)$ equals
  • ✓
    $1 - \frac{3}{{{e^2}}}$
  • B
    $\frac{3}{{{e^2}}}$
  • C
    $\frac{2}{{{e^2}}}$
  • D
    $0$
✓

Answer

Correct option: A.
$1 - \frac{3}{{{e^2}}}$
a
(a) $P(x > 1.5) = 1 - P(x = 0) - P(x = 1)$
$P(x = k) = {e^{ - \lambda }}\frac{{{\lambda ^k}}}{{k!}}$
$\therefore$ $P(x > 1.5) = 1 - \frac{1}{{{e^2}}} - \frac{2}{{{e^2}}} = $ $1 - \frac{3}{{{e^2}}}$.

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 "M.C.Q (1 Marks)" from 13. probability→13. probability — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Suppose $A$ is $3 \times 3$ matrix consisting of integer entries that are chosen at random from the set $\{-1000,-999, \ldots 999,1000\}$. Let $P$ be the probability that either $A^2=-I$ or $A$ is diagonal, where $I$ is the $3 \times 3$ identity matrix. Then,
→
Refer to Question 18 maximum of Z occurs at:
→
A tetrahedron has vertices at $O(0,\,0,\,0)$, $A(1,\,2,\,1),B(2,\,1,\,3)$ and $C( - 1,\,1,\,2)$. Then the angle between the faces $OAB$ and $ABC$will be
→
Minimise $\text{Z}=\sum\limits^{\text{n}}_{\text{j}=1}\sum\limits^{\text{m}}_{\text{i}=1}\text{c}_{\text{ij}}\cdot\text{x}_{\text{ij}}$ Subject to $\sum\limits^{\text{m}}_{\text{i}=1}\text{x}_{\text{ji}}=\text{b}_{\text{j}},\text{j}=1,2,....\text{n}$ $\sum\limits^{\text{n}}_{\text{j}=1}\text{x}_{\text{ji}}=\text{b}_{\text{j}},\text{j}=1,2,.....,\text{m}$  is a LPP with number of constraints.
  1. $\text{m}-\text{n}$
  2. $\text{m}\text{n}$
  3. $\text{m}+\text{n}$
  4. $\frac{\text{m}}{\text{n}}$
→
The value of$\int_{}^{} {{e^x}{{\sec }^2}({e^x})\;dx} $ is
→
The solution of the differential equartion $\frac{\text{dy}}{\text{dx}}-\frac{\text{y}(\text{x}+1)}{\text{x}}=0$ is given by:
  1. $\text{y}=\text{xe}^{\text{x}+\text{C}}$
  2. $\text{x}=\text{ye}^{\text{x}}$
  3. $\text{y}=\text{x}+\text{c}$
  4. $\text{xy}=\text{e}^{\text{x}}+\text{C}$ 
→
Choose the correct answer in the following:
The area bounded by the y-axis, y = cos x and y = sin x when $0\leq\text{x}\leq\frac{\pi}{2}$
  1. $2(\sqrt2-1)$
  2. $\sqrt2-1$
  3. $\sqrt2+1$
  4. $\sqrt2.$
→
If $\text{y}=\tan^{-1}\Big(\frac{\sin\text{x}+\cos\text{x}}{\cos\text{x}-\sin\text{x}}\Big),$ then $\frac{\text{dy}}{\text{dx}}$ is equals to:
  1. $\frac{1}{2}$
  2. 0
  3. 1
  4. None of these.
→
Let X1 and X2 are optimal solutions of a LPP, then:
→
The cartesian equation of line which is parallel to $3 \hat{i}+2 \hat{j}-8 \hat{k}$ and passes through the point $(5,2,-4)$ is __________ .
→