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CBSE Questions for Class 12 Commerce Applied Mathematics Probability Distribution And Its Mean And Variance Quiz 1 - MCQExams.com

The p.m.f.of a r.v. X is as follows ;
P(X=0)=3K3,P(X=1)=4K10K2,P(X=2)=5K1,P(Xx)=0 for any other value of x. then k is equal to 
  • 1
  • 2
  • 13
  • 23
Variance of the random variable X is 4. Its mean is 2. Then E(X2) is:
  • 6
  • 8
  • 2
  • 4
Another name for the mean of a probability distribution is expected value.
  • True
  • False
The variance of the random variable x whose probability distribution is given by
X=xi:1,0,+1
p(X=xi):0.4, 0.2,   0.4 is
  • 0.4
  • 0.6
  • 0.8
  • 1.0
To define probability disribution function we assign to each variable  
  • the respective probabilities
  • the specific random values
  • some integers
  • none
Out of following which are random variables
  • x= "Number of heads when two coins are tossed.
  • x="Sum of digits on uppermost face of two dice"
  • solution of " X-4=0"
  • x= "Raining"
Given E(X + c) = 8 and E(X - c) = 12 then the value of c is
  • -2
  • 4
  • -4
  • 2
Which of the following is an example of a random experiment?
  • Selecting a card from a pack of playing cards.
  • Measuring the weight of a person.
  • Finding the length of your pencil box.
  • Throwing two coins together.
To verify Pythagoras theorem is a random experiment.
  • True
  • False
The mathematical expectation of sum of points when we throw n symmetrical dice is
  • 7n
  • 7\displaystyle \times\frac{n}{2}
  • \displaystyle \frac{n}{2}
  • \displaystyle \frac{7n}{3}
Difference between sample space and subset of sample space is considered as
  • numerical complementary events
  • equal compulsory events
  • complementary events
  • compulsory events
In the p.d.f. of a random variable of three missing entries are in the ratio 1:2:3.
X=x12345
P(X=x)\dfrac{1}{10}---\dfrac{3}{20}
Then the missing entries are?
  • \dfrac{1}{5}, \dfrac{2}{5}, \dfrac{3}{5}
  • \dfrac{3}{12}, \dfrac{4}{15}, \dfrac{6}{15}
  • \dfrac{1}{10}, \dfrac{2}{10}, \dfrac{3}{10}
  • \dfrac{1}{8}, \dfrac{2}{8}, \dfrac{3}{8}
A random variable X has the probability distribution X: 1, 2, 3, 4, 5, 6, 7, 8
P(X): 0.15, 0.23, 0.12, 0.10 ,0.20 ,0.08 ,0.07 ,0.05 . For the events \mathrm{E}= \{X is a prime number \} and \mathrm{F}=\{\mathrm{X}<4\}, the probability \mathrm{P}(\mathrm{E}\cup\mathrm{F}) is: 
  • 0.87
  • 0.77
  • 0.35
  • 0.50
Statement 1: The variance of first \mathrm{n} even natural numbers is \displaystyle \frac{\mathrm{n}^{2}-1}{4}
Statement 2: The sum of first \mathrm{n} natural numbers is \displaystyle \frac{\mathrm{n}(\mathrm{n}+1)}{2} and the sum of squares of first \mathrm{n} natural numbers is \displaystyle \frac{\mathrm{n}(\mathrm{n}+1)(2\mathrm{n}+1)}{6}
  • Statement 1 is true, Statement2 is true,Statement 2 is a correct explanation for Statement 1
  • Statement 1 is true, Statement2 is true;Statement2 is not a correct explanation for statement 1
  • Statement 1 is true, Statement 2 is false.
  • Statement 1 is false, Statement 2 is true
A random variable X has its range X = \{3, 2, 1\} with the probabilities,
\dfrac{1}{2},\dfrac{1}{3} and \dfrac{1}{6} respectively. The mean value of X is
  • \dfrac{5}{3}
  • \dfrac{7}{3}
  • 3
  • 4
Four different objects 1,2,3,4 are distributed at random in four places marked 1,2,3,What is the probability that none of the objects occupy the place corresponding to its number ?
  • \frac{17}{24}
  • \frac{3}{8}
  • \frac{1}{2}
  • \frac{5}{8}
If the range of the random variable X is from a to \mathrm{b},\ \mathrm{a}<\mathrm{b},\ \mathrm{F}(\mathrm{X}<\mathrm{a})=
  • 0
  • 1
  • 0.5
  • 3
The cumulative distribution function of a random variable x is defined as
  • P(X < x)
  • P(X \ge x)
  • P(X \le x)
  • P(X > x)
An urn contains 5 red and 2 black balls. Two balls are randomly drawn. Let X represent the number of black balls. What are the possible values of X ? Is X a random variable ?
  • 0,1,2
  • 3,5,7
  • 7,7,8
  • 1,5,7
If an unbiased coin is tossed once, then the two events of getting a Head and a Tail are -
  • Mutually exclusive
  • Exhaustive
  • Equally likely
  • All of these
If a random variable X takes value 0 and 1 with respective probabilities \dfrac{2}{3} and \dfrac{1}{3} , then the expected value of X is
  • \dfrac{2}{3}
  • \dfrac{1}{3}
  • 0
  • 1
In a class of 80 students, 48 are boys and the rest of the students are girls. If 10 students shift to the other class room and a student is selected at random from the remaining class, what is the probability that a girl is selected ?
  • 11/35
  • 27/70
  • 11/40
  • Cannot be determined

10 different books and 2 different pens are given to 3 boys so that each gets equal number of things. The probability that the same boy does not receive both the pens is

  • \frac{5}{11}
  • \frac{7}{11}
  • \frac{2}{3}
  • \frac{8}{11}
If the range of the random variable X is from a to b then F(X\leq b) is
  • 0
  • 1
  • 0.5
  • 3
Expected number of heads when we toss n unbiased coins is
  • 2n
  • n
  • \dfrac{n}{2}
  • \dfrac{n}{4}
In 5 throws of a die, getting 1 or 2 is a success. The mean number of successes is
  • \dfrac{5}{3}
  • \dfrac{3}{5}
  • \dfrac{5}{9}
  • \dfrac{9}{5}
Which of the following is NOT a random experiment ?
  • Rolling an unbiased dice
  • Tossing a fair coin
  • Drawing a card from a well shuffled pack of 52 card
  • None of these
The probability distribution of a discrete random variable X is:
X = x12345
P(X = x)k2k3k4k5k
Find P (X\leq 4)
  • \cfrac 23
  • \cfrac 34
  • \cfrac 45
  • \cfrac 56
Which of the following is not a random experiment?
  • Tossing a coin
  • Rolling a dice
  • Choosing a card from a deck of 52 cards
  • Throw a stone from a roof of a building
Which of the following is an random experiment?
  • Rolling a pair of dice
  • Choosing 2 marbles from a jar
  • Choosing a number at random from 1 to 10
  • Tossing two coins
0:0:5


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Practice Class 12 Commerce Applied Mathematics Quiz Questions and Answers