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PART 2 : RANDOM VARIABLE ANE DISCRETE PROBABILITY DISTRIBUTION · Gujarat Board (GSEB) STD 12 Commerce (GSEB - English Medium). 23 questions.

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23 questions · timed · auto-graded

MCQ 11 Mark
If $n=12$ and $p=\frac{3}{8}$ for a binomial distribution, what will be its mean ?
  • ✓
    $4.5$
  • B
    $7.5$
  • C
    $6$
  • D
    $2.81$
Answer
Correct option: A.
$4.5$
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MCQ 21 Mark
The mean of a binomial distribution is $2 .$ If the probability of success for it is $0.4$, what will be its variance?
  • A
    $0.8$
  • B
    $0.2$
  • ✓
    $1.2$
  • D
    $0.48$
Answer
Correct option: C.
$1.2$
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MCQ 31 Mark
Which of the following is true for a binomial distribution ?
  • ✓
    Mean $=$ Variance
  • B
    Mean $=($Variance$)^2$
  • C
    Mean $ > $ Variance
  • D
    Mean $ < $ Variance
Answer
Correct option: A.
Mean $=$ Variance
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MCQ 41 Mark
What will be the expected value of the number of heads when $4$ unbiased coins are thrown together ?
  • ✓
    $2$
  • B
    $1$
  • C
    $0.5$
  • D
    $4$
Answer
Correct option: A.
$2$
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MCQ 51 Mark
If the mean of a binomial distribution $b(6, p)$ has mean $3,$ what can be said about the skewness of the distribution ?
  • A
    Positive skewness
  • ✓
    Symmetric
  • C
    Negative skewness
  • D
    Nothing can be said
Answer
Correct option: B.
Symmetric
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MCQ 61 Mark
The variance of a binomial variable is $4.$ What can be said about the skewness of the distribution?
  • A
    Positive skewness
  • B
    Negative skewness
  • C
    Symmetric
  • ✓
    Nothing can be said
Answer
Correct option: D.
Nothing can be said
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MCQ 71 Mark
Which of the following is true for a binomial distribution with negative skewness ?
  • A
    Mean $=\frac{n}{2}$
  • B
    Mean $ >\frac{n}{2}$
  • C
    Mean $-n$
  • ✓
    Mean $ <\frac{n}{2}$
Answer
Correct option: D.
Mean $ <\frac{n}{2}$
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MCQ 81 Mark
Which of the following is true for a binomial distribution $b(n, p)$ with positive skewness?
  • ✓
    $p<\frac{1}{2}$
  • B
    $p>\frac{1}{2}$
  • C
    $p=\frac{1}{2}$
  • D
    $p=0$
Answer
Correct option: A.
$p<\frac{1}{2}$
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MCQ 91 Mark
What will be the probability of getting I success in a binomial distribution $b(n, p)$ ?
  • A
    $n p q$
  • B
    $n p q^n$
  • ✓
    $n p^n q$
  • D
    $n p q^{n-1}$
Answer
Correct option: C.
$n p^n q$
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MCQ 101 Mark
If variable $X=$ number of heads in a random experiment of tossing two coins, which of the following will be the set values of $X$ ?
  • ✓
    $\{0,1\}$
  • B
    $\{0,1,2\}$
  • C
    $\{0,2\}$
  • D
    $\{1,2\}$
Answer
Correct option: A.
$\{0,1\}$
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MCQ 111 Mark
State the parameters of binomial distribution.
  • A
    $n$ and $p$
  • ✓
    $n p$ and $n q$
  • C
    $p$ and $q$
  • D
    $n p$ and $n p q$
Answer
Correct option: B.
$n p$ and $n q$
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MCQ 121 Mark
Which of the following values are possible for a binomial variable $X$ with parameters $n$ and $p$.
  • A
    $x=1,2, \ldots, n$
  • B
    $0 \leq x \leq n$
  • C
    $x=0,1,2, \ldots, n$
  • ✓
    $x=0, I , 2, \ldots \ldots$
Answer
Correct option: D.
$x=0, I , 2, \ldots \ldots$
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MCQ 141 Mark
If the probabilities of a random variable $X$ assuming only two values $-3$ and $6$ are $\frac{1}{3}$ and $\frac{2}{3}$ respectively, what is the expected values of $X$ ?
  • A
    $3$
  • B
    $5$
  • ✓
    $0$
  • D
    $1$
Answer
Correct option: C.
$0$
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MCQ 151 Mark
The possible values of a discrete variable are $1,2,3$ and $4 .$ If $p( l )=p(2)=p(3)=0.3$. find $p(4)$.
  • A
    $0.1$
  • ✓
    $0.3$
  • C
    $0.7$
  • D
    $0$
Answer
Correct option: B.
$0.3$
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MCQ 161 Mark
A random variable $X$ assumes only three values $x_1, x_2$ and $x_3$. Which of the following can be a probability distribution of variable $X$ ?
  • ✓
    $p\left(x_1\right)=0.4, \quad p\left(x_2\right)=0.3, \quad p\left(x_3\right)=0.5$
  • B
    $p\left(x_1\right)=0.4, \quad p\left(x_2\right)=0.4, \quad p\left(x_3\right)=0.2$
  • C
    $p\left(x_1\right)=0.4, \quad p\left(x_2\right)=0.8, \quad p\left(x_3\right)=0.1$
  • D
    $p\left(x_1\right)=p\left(x_2\right)=p\left(x_3\right)=0.2$
Answer
Correct option: A.
$p\left(x_1\right)=0.4, \quad p\left(x_2\right)=0.3, \quad p\left(x_3\right)=0.5$
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MCQ 171 Mark
A random variable $X$ assumes only three values $a, b, c$ with respective probabilities $3 k, 5 k$ and $2 k(k>0)$. What will be the value of $k$ ?
  • A
    $10$
  • ✓
    $0.01$
  • C
    $1$
  • D
    $0.1$
Answer
Correct option: B.
$0.01$
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MCQ 181 Mark
If $p\left(x_j\right)$ are the probabilities of values $x_j$ of the variable $X$ for a discrete probability distribution, which of the following statements is true ?
  • A
    $-1$
  • B
    $0$
  • C
    $0$
  • ✓
    $-1$
Answer
Correct option: D.
$-1$
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MCQ 191 Mark
What is the total probability for a discrete probability distribution?
  • A
    $0$
  • B
    $-1$
  • C
    $2$
  • ✓
    $1$
Answer
Correct option: D.
$1$
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MCQ 201 Mark
The values of a variable are natural numbers. What type of variable is it ?
  • A
    Continuous variable
  • B
    Control variable
  • ✓
    Discrete variable
  • D
    Qualitative variable
Answer
Correct option: C.
Discrete variable
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MCQ 211 Mark
Which of the following variable is not a discrete random variable?
  • A
    Number of typing errors per page of a book
  • B
    Weight of students
  • ✓
    Number of children per family
  • D
    Number of accidents on the road
Answer
Correct option: C.
Number of children per family
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MCQ 221 Mark
Which of the following variable is an illustration of a continuous variable ?
  • A
    Number of units shown in the electricity bill of a family
  • ✓
    Number of vehicles at a given time in a parking lot
  • C
    Time taken by every student for Statistics paper
  • D
    Number of passengers in an ST bus
Answer
Correct option: B.
Number of vehicles at a given time in a parking lot
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MCQ 231 Mark
Which of the following variable is an illustration of a discrete variable ?
  • A
    Number of children born in a hospital on a certain day
  • ✓
    Density of water in the reservoir of a dam
  • C
    Weight of an apple selected from a box
  • D
    Area of farms in a village
Answer
Correct option: B.
Density of water in the reservoir of a dam
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