CBSE Questions for Class 12 Commerce Applied Mathematics Probability Distribution And Its Mean And Variance Quiz 4 - MCQExams.com

The range of a random variable X is $${1, 2, 3, 4, ..}$$ and the probabilities are $$P(X=K)=\dfrac{3^{CK}}{\angle K};$$
$$K=1,2,3,4$$,......,then the value of C is
  • $$log_{e}3 $$
  • $$log_{e} 2 $$
  • $$log_{3}(log_{e}2) $$
  • $$log_{2}(log_{e}3) $$
 The range of a random variable $$\mathrm{X}$$ is $$\left\{ 0,\quad 1,\quad 2 \right\} $$ and $$\mathrm{P}(\mathrm{X}=0)=3\mathrm{K}^{3},\mathrm{P}(\mathrm{X}=1)=4\mathrm{K}-10\mathrm{K}^{2}
$$
$$\mathrm{P}(\mathrm{x}=2)=5\mathrm{K}-1$$. Then we have
  • $$\mathrm{P}(\mathrm{X}=0)<\mathrm{P}(\mathrm{X}=2)<\mathrm{P}(\mathrm{X}=1)$$
  • $$\mathrm{P}(\mathrm{X}=0)<\mathrm{P}(\mathrm{X}=1)<\mathrm{P}(\mathrm{X}=2)$$
  • $$\mathrm{P}(\mathrm{X}=1)+\mathrm{P}(\mathrm{X}=0)=\mathrm{P}(\mathrm{X}=2)$$
  • $$\mathrm{P}(\mathrm{X}=1)>\mathrm{P}(\mathrm{X}=0)+\mathrm{P}(\mathrm{X}=2)$$
Write the probability distribution when three coins are tossed.
  • $$X\quad \quad \quad :\begin{matrix} 0 & 1 & \quad 2 & 3 \end{matrix}\quad \\ P(X)\quad :\quad \begin{matrix} \cfrac { 1 }{ 8 } & \cfrac { 3 }{ 8 } & \cfrac { 3 }{ 8 } & \cfrac { 1 }{ 8 } \end{matrix}$$
  • $$X\quad \quad \quad :\begin{matrix} 0 & 1 & \quad 2 & 3 \end{matrix}\quad \\ P(X)\quad :\quad \begin{matrix} \cfrac { 1 }{ 8 } & \cfrac { 3 }{ 8 } & \cfrac { 5 }{ 8 } & \cfrac { 7 }{ 8 } \end{matrix}$$
  • $$X\quad \quad \quad :\begin{matrix} 0 & 1 & \quad 2 & 3 \end{matrix}\quad \\ P(X)\quad :\quad \begin{matrix} \cfrac { 7 }{ 8 } & \cfrac { 5 }{ 8 } & \cfrac { 3 }{ 8 } & \cfrac { 1 }{ 8 } \end{matrix}$$
  • $$X\quad \quad \quad :\begin{matrix} 0 & 1 & \quad 2 & 3 \end{matrix}\quad \\ P(X)\quad :\quad \begin{matrix} \cfrac { 1 }{ 8 } & \cfrac { 3 }{ 8 } & \cfrac { 5 }{ 8 } & \cfrac { 1 }{ 8 } \end{matrix}$$
A player tosses two fair coins. He wins $$Rs.\ 5/-$$ if two heads occur, $$Rs.$$ $$2/-$$ if one head occurs and $$Rs.$$ $$1/-$$ if no head occurs. Then his expected gain is
  • $$Rs.\dfrac{8}{3}$$
  • $$Rs.\dfrac{7}{3}$$
  • $$Rs.2.5$$
  • $$Rs.1.5$$
The probability of age of the workers to be 40 years or more is:
  • $$0.275$$
  • $$0.475$$
  • $$0.675$$
  • $$0.975$$
$$X$$ 1 2 3 4 5 6 7 8 
$$P(X)$$ 15 23 12 10 20 8 7 5 
A random variable $$X$$ has the probability distribution for the event $$\displaystyle E=\{ X$$  is a prime number $$ \}$$. If $$\displaystyle F=\left\{X<4\right\}$$, then the probability $$\displaystyle P(E\cup F)$$ is
  • $$\displaystyle 0.40$$
  • $$\displaystyle 0.77$$
  • $$\displaystyle 0.57$$
  • $$\displaystyle 0.45$$
Which set is shaded in the above diagram?
377437.png
  • $$A\cap C$$
  • $$A\cap B\cap C$$
  • $$A\cup(B\cap C)$$
  • $$A\cap(B\cup C)$$
Expectation of $$X$$ equals
  • $$6$$
  • $$12$$
  • $$8$$
  • None of these
South African cricket captain lost the toss of a coin 13 times out ofThe chance of this happening was
  • $$\displaystyle \frac{7}{2^{13}}$$
  • $$\displaystyle \frac{1}{2^{13}}$$
  • $$\displaystyle \frac{13}{2^{14}}$$
  • $$\displaystyle \frac{13}{2^{13}}$$
A fair die is tossed repeatedly until a six is obtained. Let $$X$$ denote the number of tosses required. The probability that $$X\geq 3$$ equals
  • $$\displaystyle \frac {125}{216}$$
  • $$\displaystyle \frac {25}{36}$$
  • $$\displaystyle \frac {5}{36}$$
  • $$\displaystyle \frac {25}{216}$$
Let $$X$$ represent the difference between the number of heads and the number of tails obtained when a coin is tossed $$6$$ times. What are possible values of $$X$$ ?
  • $$9,7,4,0$$
  • $$0,2,4,6$$
  • $$6,7,7,2$$
  • $$6,4,2,0$$
The probability distribution of a random variable is given below:
$$X = x$$$$0$$$$1$$$$2$$$$3$$$$4$$$$5$$$$6$$$$7$$
$$P(X = x)$$$$0$$$$K$$$$2K$$$$2K$$$$3K$$$$K^{2}$$$$2K^{2}$$$$7K^{2} + K$$
Then $$P(0 < X < 5) =$$
  • $$\dfrac {1}{10}$$
  • $$\dfrac {3}{10}$$
  • $$\dfrac {8}{10}$$
  • $$\dfrac {7}{10}$$
If p.d.f. of continuous r.v. is given by
$$\displaystyle f\left( x \right) =\frac { x }{ 8 } ,0<x<4$$
$$\displaystyle =0$$, otherwise then F(x) is
  • $$\displaystyle \frac { { x }^{ 2 } }{ 8 } $$
  • $$\displaystyle \frac { x }{ 4 } $$
  • $$\displaystyle \frac { { x }^{ 2 } }{ 4 } $$
  • $$\displaystyle \frac { { x }^{ 2 } }{ 16 } $$
Let $$\displaystyle f\left( x \right) =\left\{ \begin{matrix} \dfrac { 1 }{ { x }^{ 2 } } ;1<x<\infty  \\ 0;\text{otherwise} \end{matrix} \right\} $$, be the probability density function of random variable X, then the value of $$\displaystyle P\left( -2\le x\le 2 \right) $$ is
  • $$2$$
  • $$\log2$$
  • $$\displaystyle \frac { 1 }{ 2 } $$
  • $$0$$
The mean of the numbers obtained on throwing a die having written 1 on three faces, $$2$$ on two faces and $$5$$ on one face is:
  • $$1$$
  • $$2$$
  • $$5$$
  • $$\displaystyle\frac{8}{3}$$
The probability distribution of $$x$$ is
$$x$$$$0$$$$1$$$$2$$$$3$$
$$P(x)$$$$0.2$$$$k$$$$k$$$$2k$$
find the value of $$k$$
  • $$0.2$$
  • $$0.3$$
  • $$0.4$$
  • $$0.1$$
Suppose that two cards are drawn at random from a deck of cards. Let $$X$$ be the number of aces obtained. Then the value of $$E\left(X\right)$$ is
  • $$\displaystyle\frac{37}{221}$$
  • $$\displaystyle\frac{5}{13}$$
  • $$\displaystyle\frac{1}{13}$$
  • $$\displaystyle\frac{2}{13}$$
For the probability distribution function of random variable X ,$$x_1,x_2,x_3,....x_n $$ are the values X takes, and $$p(x_i) $$  denote the probability of $$x_i$$ then which one of the following is true.?
  • $$p(x_i)>0$$
  • $$p(x_i)<0$$
  • $$\sum p(x_i)=1$$
  • $$\sum x_i=1$$
The  following is probabilty distribution of r.v X.
x123456
p(x)$$\frac{k}{6}$$$$\frac{k}{6}$$$$\frac{k}{6}$$$$\frac{k}{6}$$$$\frac{k}{6}$$$$\frac{k}{6}$$
then value of k is
  • $$0$$
  • $$1$$
  • $$2$$
  • $$3$$
Choose the discrete random varaiable of the following.
  • Number of heads on a coin
  • Sum of digits of uppermost face when two dice are rolled
  • Height of students
  • Weight of students
The variable which takes some specific values is called
  • discrete random variable
  • continuous random variable
  • both A and B
  • none
Choose the contineous random variable of the following:
  • Number of heads on a coin
  • Sum of digits of uppermost face when two dice are rolled
  • Height of students
  • Weight of students
A biased coin is tossed twice.The probability of head is twice the tail.The PDF of number of heads is
x$$0$$$$1$$$$2$$
p(x)$$\dfrac{a}{d}$$$$\dfrac{b}{d}$$$$\dfrac{c}{d}$$
then values of $$a,b,c,d$$ are 
  • $$a=1,b=2,c=3,d=4$$
  • $$a=1,b=4,c=4,d=9$$
  • $$a=1,b=4,c=4,d=10$$
  • $$a=1,b=2,c=1,d=4$$
The variable which assumes all possible values in the given interval is called
  • discrete random variable
  • continuous variable
  • both A and B
  • none
Which of the following is correct regarding probability mass function?
  • All probabilities are positive.
  • Any event in the distribution has a probability of happening of between 0 and 1.
  • Both are correct
  • None of the above
The probability function is always
  • Negative
  • Non negative
  • Positive
  • None

Standard normal probability distribution has mean equal to $$40$$, whereas value of random variable x is $$80$$ and z-statistic is equal to $$1.8$$ then standard deviation of standard normal probability distribution is
    • $$150$$
    • $$80$$
    • $$40$$
    • $$11.11$$
    The PDF of variable x: number of times sum 6 appears on in two throw of a pair of dice is
    x$$0$$$$1$$$$2$$
    p(x)$$a$$$$b$$$$c$$
    then values of $$a,b,c$$ are.
    • $$a=\dfrac{2}{36},b=\dfrac{3}{36},c=\dfrac{5}{36}$$
    • $$a=\dfrac{961}{36},b=\dfrac{310}{36},c=\dfrac{25}{36}$$
    • $$a=\dfrac{961}{1269},b=\dfrac{310}{1296},c=\dfrac{25}{1296}$$
    • $$a=\dfrac{91}{36},b=\dfrac{30}{36},c=\dfrac{25}{36}$$
    From $$30$$ bulbs out of which $$10$$ are defective, $$3$$ bulbs are chosen. X denotes number of defective bulbs.The PDF of r.v x is
    x0123
    p(x)57k95k45k6k
    then k is
    • $$\dfrac{1}{210}$$
    • $$\dfrac{2}{203}$$
    • $$\dfrac{1}{203}$$
    • $$\dfrac{1}{29}$$
    The following is the p.d.f. (probability density function) of a continuous random variable $$X$$:
    $$f(x) = \dfrac {x}{32}, 0 < x < 8 = 0$$, otherwise
    Find the expression for c.d.f. (cumulative distribution function) of $$X$$
    • $$\cfrac {x^2}{64}-1$$
    • $$\cfrac {x^2}{64}$$
    • $$\cfrac {x+1}{64}$$
    • $$\cfrac {x^2-1}{64}$$
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