MCQ Questions for Class 12 Commerce Applied Mathematics Probability Distribution And Its Mean And Variance Quiz 8

Consider the following probability distribution :

$X_{i}$	$1$	$3$	$5$	$6$
$P_{i}$	$0.1$	$0.2$	$0.4$	$0.3$

Then

$E(X)=$

0%
$4.5$
0%
$5.5$
0%
$6.5$
0%
$7.5$

P(x) is a polynomial satisfying P(x+3/2)=p(x) for all real values of x. If P(5)=2010, what is the value of P(8)

0%
$2008$
0%
$2009$
0%
$2010$
0%
None of these

For the following probability distribution.

$X=x$	$1$	$0$	$4$
P	$1/2$	$3/8$	$1/8$

The value of

$E[X-E(X)]$ is?

0%
$1$
0%
$1/2$
0%
$0$
0%
$1/4$

The following is the c.d.f. of a discrete r.v. X:

X	$-3$	$-1$	$0$	$1$	$3$	$5$	$7$	$9$
$F(x)$	$0.1$	$0.3$	$0.5$	$0.65$	$0.75$	$0.85$	$0.90$	$1$

Find

$P(X =-3/X < 0)$ .

0%
$0.3333$
0%
$0.35$
0%
$0.55$
0%
$0.25$

Explanation

$\alpha_i$	$f(x)$	$P(X = x_i)$
$-3$ $-1$ $0$ $1$ $3$ $5$ $7$ $9$	$0.1$ $0.3$ $0.5$ $0.65$ $0.76$ $0.85$ $0.90$ $1$	$0.1$ $0.2$ $0.2$ $0.15$ $0.1$ $0.1$ $0.05$ $0.1$

$P\left( X=-3\right) =0.1$

$\Rightarrow P\left( X<0\right) =P\left( X=-1\right) +P\left( X=-3\right)$

$=0.2+0.1$

$\Rightarrow \dfrac{P\left( X=-3\right)}{P\left( X<0\right) }=\dfrac{0.1}{0.3}=0.3333$

Hence, the answer is

$0.3333.$

Two cards are drawn successive with replacement from a pack of cards. Taking the random variable X= the variance of X is

0%
$\dfrac{2}{13}$
0%
$\dfrac{9}{13}$
0%
$\dfrac{24}{169}$
0%
$\dfrac{1}{13}$

X is a continuous random variable with probability density function

$f(x) = 3 (1 - 2x^2)$ ; 0 < x < 1
= 0 ; otherwise
Then, value of

$P \left(\dfrac{1}{4} < X < \dfrac{1}{3} \right)$ is

0%
$\dfrac{128}{752}$
0%
$\dfrac{331}{752}$
0%
$\dfrac{165}{864}$
0%
$\dfrac{179}{864}$

$P(X=x)=C \left(\dfrac{2}{3}\right)^{x}; x=1,2,3,4,.......$ is a probability mass function, the value of

$C$ is

0%
$\dfrac{1}{4}$
0%
$\dfrac{1}{3}$
0%
$\dfrac{1}{2}$
0%
$\dfrac{1}{6}$

If the range of a random variable

$X$ is

${0,\ 1,\ 2,\ 3,....}$ with

$P{X=K}=\dfrac {(k+1)a}{3^{k}}$ for

$k\ge 0$ , then

$a=$

0%
$2/3$
0%
$4/9$
0%
$89/27$
0%
$16/81$

The c.d.f of a discrete r.v X isThen

$P\left(X=-3|X<0\right)$

0%
$0.3333$
0%
$0.35$
0%
$0.55$
0%
$0.25$

Two coins are tossed 1000 times and the outcomes are recorded as below:

Number of heads	2	1	0
Frequency	200	550	250

Based on this information, the probability for atmost one head is

0%
$\frac{1}{5}$
0%
$\frac{1}{4}$
0%
$\frac{4}{5}$
0%
$\frac{3}{4}$

A fair die is tossed repeatedly until a 6 is obtained. Let X denote the number of tosses required.

The probability that

$x \geq 3$ equals

0%
125/216
0%
25/36
0%
5/36
0%
25/216

An unbiased coin is tossed n times. Let X denote the number of times head occurs. If P(X=4), P(X=5) and P(X=6) are in AP, then the value of n can be

0%
9
0%
10
0%
12
0%
14

$f(x)=k\sqrt {k}, 0 < x < 1=0$ , otherwise is p.d.f of

$X$ . Then

$P(0.3 < X < 0.6)=$ ____

0%
$(0.6-0.3)^{\dfrac {3}{2}}$
0%
$(0.3-0.6)^{\dfrac {3}{2}}$
0%
$(0.6)^{\dfrac {3}{2}}-(0.3)^{\dfrac {3}{2}}$
0%
$(0.3)^{\dfrac {3}{2}}-(0.6)^{\dfrac {3}{2}}$

Three coins are thrown simultaneously 60 times, with the following frequencies:

No. of heads	3	2	1	0
Frequency	10	5	18	27

Based on these information find the probability of

0%
P (getting 3 heads)
0%
P (getting no heads)
0%
P (at most 1 head)
0%
P (at least 1 head)

CBSE Questions for Class 12 Commerce Applied Mathematics Probability Distribution And Its Mean And Variance Quiz 8 - MCQExams.com

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Practice Class 12 Commerce Applied Mathematics Quiz Questions and Answers

CBSE Questions for Class 12 Commerce Applied Mathematics Probability Distribution And Its Mean And Variance Quiz 8 - MCQExams.com

0:0:1

Practice Class 12 Commerce Applied Mathematics Quiz Questions and Answers

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