CBSE Questions for Class 12 Commerce Applied Mathematics Probability Distribution And Its Mean And Variance Quiz 2 - MCQExams.com

A ______ experiment is a process whose outcome is undetermined.
  • variable
  • random
  • event
  • sample
In which experiment outcomes are not predictable?
  • sample
  • event
  • random
  • essential
A box contains 3 white and 2 black balls. Two balls are drawn at random one after the other. If the balls are not replaced. what is the probability that both the balls are black ?
  • $$\dfrac{2}{5}$$
  • $$\dfrac{1}{5}$$
  • $$\dfrac{1}{10}$$
  • None of the above
The probability that a leap year will have $$53$$ sundays is 
  • $$1/7$$
  • $$2/7$$
  • $$5/7$$
  • $$6/7$$
The probability distribution of a discrete random variable X is given in the following table :
$$X = x$$$$0$$$$1$$$$2$$
$$P(x)$$$$4C^{3}$$$$4C - 13C^{2}$$$$7C - 1$$
; $$C > 0$$ then $$C =$$ ________.
  • $$2$$
  • $$1$$
  • $$\dfrac {1}{4}$$
  • $$1$$ and $$-\dfrac {1}{4}$$
In the following, find the value of k.
$$P(x)=\left\{\begin{matrix} kx & for & x=1, 2, 3\\ 0 & for & otherwise\end{matrix}\right.$$.
  • $$k=\dfrac 16$$.
  • $$k=\dfrac 13$$.
  • $$k=\dfrac 19$$.
  • $$k=\dfrac 15$$.
The p.d.f of a continuous random variable $$X$$ is 
$$f(x)=\begin{cases} \dfrac { x }{ 8 } ,\quad 0<x<4 \\ 0,\ \ \ otherwise \end{cases}$$
Then the value of $$P(X>3)$$ is
  • $$\dfrac{3}{16}$$
  • $$\dfrac{5}{16}$$
  • $$\dfrac{7}{16}$$
  • $$\dfrac{9}{16}$$
Find the c.d.f. $$F(x)$$ associated with the following p.d.f. $$f(x)$$:
$$f(x)\begin{matrix} =12x^2(1-x), & 0 < x < 1\\ =0, & otherwise\end{matrix}$$. Also, find $$P\left(\dfrac{1}{3} < X < \dfrac{1}{2}\right)$$ by using p.d.f. and c.d.f.
  • $$F(x)=4x^3-3x^2, P\left(\dfrac{1}{3} < X < \dfrac{1}{2}\right)=\dfrac{119}{432}$$.
  • $$F(x)=3x^3-5x^2, P\left(\dfrac{1}{3} < X < \dfrac{1}{2}\right)=\dfrac{129}{432}$$.
  • $$F(x)=4x^2-3x^2, P\left(\dfrac{1}{3} < X < \dfrac{1}{2}\right)=\dfrac{119}{432}$$.
  • $$F(x)=4x-3x^3, P\left(\dfrac{1}{3} < X < \dfrac{1}{2}\right)=\dfrac{19}{432}$$.
Two symmetrical dice are thrown $$200$$ times. Getting a sum of $$9$$ points is considered to be a success. The probability distribution of successes is
  • $$\left( 200,\ \cfrac { 1 }{ 9 } ,\ \cfrac { 8 }{ 9 } \right) $$
  • $$\left( 200,\ \cfrac { 2 }{ 9 } ,\ \cfrac { 7 }{ 9 } \right) $$
  • $$\left( 200,\ \cfrac { 4 }{ 9 } ,\ \cfrac { 5 }{ 9 } \right) $$
  • $$\left( 200,\ \cfrac { 1 }{ 4 } ,\ \cfrac { 3 }{ 4 } \right) $$
If the variance of the random variable $$X$$ is $$5$$, then the variance of the random variable $$-3X$$ is
  • $$15$$
  • $$45$$
  • $$-45$$
  • $$60$$
A die is tossed twice. Getting an odd number is termed a success. The probability distribution of number of successes (X) is formed. Then its mean, variance are
  • $$1,\: \displaystyle\frac{1}{2}$$
  • $$ \displaystyle\frac{1}{2},\: 1$$
  • $$ \displaystyle\frac{1}{2},\: \displaystyle\frac{1}{2}$$
  • $$1,\: 1 $$
A random variable $$X$$ takes values $$-1, 0, +1$$, Its mean is $$0.6$$ and if $$P(X=0)=0.2$$, then $$P(X=1)=$$
  • $$0.7$$
  • $$0.5$$
  • $$0.1$$
  • $$0.2$$
The standard deviation $$\sigma $$ of $$(q+p)^{16}$$ isThe mean of the distribution is
  • $$2$$
  • $$8$$
  • $$16$$
  • $$20$$
A coin is tossed successively until for the $$1$$st time head occurs. The expected number of tosses required is
  • $$4$$
  • $$2$$
  • $$1$$
  • $$5$$
A random variable $$X$$ takes the values $$0, 1$$ and $$2$$. If $$P(X=1)=P(X=2)$$ and $$P(X=0)=0.4$$, then the mean value of the random variable $$X$$ is
  • $$0.2$$
  • $$0.5$$
  • $$0.7$$
  • $$0.9$$
A fair die is rolled $$180$$ times. The expected number of $$6$$ is
  • $$50$$
  • $$30$$
  • $$10$$
  • $$5$$
The mean or average number of points when we throw a symmetrical die is
  • $$14$$
  • $$7$$
  • $$7/2$$
  • $$14/3$$
The mathematical expectation of sum of points when $$ 2$$ symmetrical dice are rolled is
  • $$14$$
  • $$7$$
  • $$7/2$$
  • $$14/3$$
In a business venture a man can make a profit of Rs. $$2000/-$$ with probability of $$0.4$$ or have a loss of Rs. $$1000/-$$ with probability 0.His expected profit is
  • Rs. $$800/-$$
  • Rs. $$600/-$$
  • Rs. $$200/-$$
  • Rs. $$400/-$$
A random variable $$X$$ takes values $$-1, 0, +1$$. Its mean is $$0.6$$. If $$P(X=0)=0.2$$, then $$P(X=1)=$$
  • $$0.1$$
  • $$0.3$$
  • $$0.7$$
  • $$0.6$$
$$4$$ bad apples accidentally got mixed up with $$20$$ good apples. In a draw of $$2$$ apples at random, expected number of bad apples is
  • $$1$$
  • $$2/3$$
  • $$1/3$$
  • $$1/6$$
An urn A contains 4 white and 6 red balls. Three balls are drawn at random the expected number of red balls drawn is
  • 3.0
  • 1.8
  • 1.2
  • 1.6
The probability that there would be $$1, 2$$ or $$3$$ persons riding a bicycle are $$0.85, 0.12$$ and $$0.03$$ respectively. The expected number of persons per bicycle is
  • $$2$$
  • $$1$$
  • $$1.18$$
  • $$3$$
Two cards are drawn simultaneously from a well shuffled pack of $$52$$ cards. The expected number of aces is
  • $$\displaystyle \frac{4}{13}$$
  • $$\displaystyle \frac{3}{13}$$
  • $$\displaystyle \frac{2}{13}$$
  • $$\displaystyle \frac{1}{13}$$
Three coins whose faces are marked $$1$$ and $$2$$ are tossed. The expected sum of numbers on their faces is
  • $$4$$
  • $$4.5$$
  • $$5$$
  • $$6$$
Two unbiased coins whose faces are marked $$1$$ and $$2$$ are tossed. The mean value of the total of the numbers is
  • $$3$$
  • $$4$$
  • $$5$$
  • $$2$$
An urn A contains 4 white and 6 red balls. Three balls are drawn at random the expected number of white balls drawn is
  • $$3.0$$
  • $$1.8$$
  • $$1.2$$
  • $$1.6$$
If it rains a dealer in rain coats can earn Rs.$$500$$/- a day. If it is fair he will lose Rs. $$40$$/- a day. His mean profit if the probability of a fair day is $$0.6$$ is:
  • Rs. $$230$$/-
  • Rs. $$460$$/-
  • Rs. $$176$$/-
  • Rs. $$88$$/-
The probability that the value of certain stock will remain the same is $$0.46$$. The probability that its value will increase by Rs. $$0.50$$ or Re. $$1$$ per share are respectively $$0.17$$ and $$0.23$$ and the probability that its value will decrease by Rs. $$0.25$$ per share is $$0.14$$. The expected gain per share is
  • Rs. $$0.75$$
  • Rs. $$0.25$$
  • Rs. $$0.28$$
  • Rs. $$0.50$$
The value of $$K$$, if the probability distribution of a discrete random variable $$x$$ is
$$X=x_{1}:1 2 3  $$
$$p(X=x_{1}):\dfrac{1}{k^{2}}\dfrac{2}{k^{2}}\dfrac{3}{k^{2}}$$
  • $$\sqrt{6}$$
  • $$-\sqrt{6}$$
  • $$\pm \sqrt{6}$$
  • 6
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