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

Consider the following probability distribution :
$$X_{i}$$$$1$$$$3$$$$5$$$$6$$
$$P_{i}$$$$0.1$$$$0.2$$$$0.4$$$$0.3$$
Then $$E(X)=$$
  • $$4.5$$
  • $$5.5$$
  • $$6.5$$
  • $$7.5$$
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)
  • $$2008$$
  • $$2009$$
  • $$2010$$
  • 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?
  • $$1$$
  • $$1/2$$
  • $$0$$
  • $$1/4$$
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 $$P(X =-3/X < 0)$$.
  • $$0.3333$$
  • $$0.35$$
  • $$0.55$$
  • $$0.25$$
Two cards are drawn successive with replacement from a pack of cards. Taking the random variable X= the variance of X is
  • $$\dfrac{2}{13}$$
  • $$\dfrac{9}{13}$$
  • $$\dfrac{24}{169}$$
  • $$\dfrac{1}{13}$$
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 
  • $$\dfrac{128}{752}$$
  • $$\dfrac{331}{752}$$
  • $$\dfrac{165}{864}$$
  • $$\dfrac{179}{864}$$
if $$P(X=x)=C \left(\dfrac{2}{3}\right)^{x}; x=1,2,3,4,.......$$ is a probability mass function, the value of $$C$$ is 
  • $$\dfrac{1}{4}$$
  • $$\dfrac{1}{3}$$
  • $$\dfrac{1}{2}$$
  • $$\dfrac{1}{6}$$
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 $$a=$$  
  • $$2/3$$
  • $$4/9$$
  • $$89/27$$
  • $$16/81$$
The c.d.f of a discrete r.v X isThen $$P\left(X=-3|X<0\right)$$
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  • $$0.3333$$
  • $$0.35$$
  • $$0.55$$
  • $$0.25$$
Two coins are tossed 1000 times and the outcomes are recorded as below:
Number of heads  2  1  0
Frequency200550250
Based on this information, the probability for atmost one head is
  • $$\frac{1}{5}$$
  • $$\frac{1}{4}$$
  • $$\frac{4}{5}$$
  • $$\frac{3}{4}$$
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 
  • 125/216
  • 25/36
  • 5/36
  • 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
  • 9
  • 10
  • 12
  • 14
$$f(x)=k\sqrt {k}, 0 < x < 1=0$$, otherwise is p.d.f of $$X$$. Then $$P(0.3 < X < 0.6)=$$  ____
  • $$(0.6-0.3)^{\dfrac {3}{2}}$$
  • $$(0.3-0.6)^{\dfrac {3}{2}}$$
  • $$(0.6)^{\dfrac {3}{2}}-(0.3)^{\dfrac {3}{2}}$$
  • $$(0.3)^{\dfrac {3}{2}}-(0.6)^{\dfrac {3}{2}}$$
Three coins are thrown simultaneously 60 times, with the following frequencies: 
No. of heads3210
Frequency1051827
Based on these information find the probability of 
  • P (getting 3 heads)
  • P (getting no heads)
  • P (at most 1 head)
  • P (at least 1 head)
0:0:1


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