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Mean and variance of a random variable Maths - Mean and variance of a random variable

Gujarat Board (GSEB) - STD 12 Science - Maths (GSEB - English Medium). 83 questions in this chapter.

Question types

Mean and variance of a random variable question types

83 questions across 5 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

83
Questions
5
Question groups
5
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Sample Questions

Mean and variance of a random variable questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
The probability distribution of a discrete random variable X is given below:

$\text{X}:$

$2$

$3$

$4$

$5$

$\text{P}(\text{X}):$

$\frac{5}{\text{k}}$

$\frac{7}{\text{k}}$

$\frac{9}{\text{k}}$

$\frac{11}{\text{k}}$

The value of k is:

  1. 8
  2. 16
  3. 32
  4. 48
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Q 2M.C.Q (1 Marks)1 Mark
Let X be a discrete random variable. Then the variance of X is:

  1. E(X2)

  2. E(X2) + (E(X))2

  3. E(X2) - (E(X))2

  4. $\sqrt{\text{E}(\text{X}^2)-(\text{E}(\text{X}))^2}$

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Q 3M.C.Q (1 Marks)1 Mark
If X is a random variable with probability distribution as given below:

X = xi 0 1 2 3
P(X = Xi) k 3k 3k k

The value of k and its variance are:

  1. $\frac{1}{8},\frac{22}{27}$

  2. $\frac{1}{8},\frac{23}{27}$

  3. $\frac{1}{8},\frac{24}{27}$

  4. $\frac{1}{8},\frac{3}{4}$

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Q 4M.C.Q (1 Marks)1 Mark
The probability distribution of a discrete random variable X is given below:

$\text{X}:$
$1$
$2$
$3$
$4$
$\text{P}(\text{X}):$
$\frac{1}{10}$
$\frac{1}{5}$
$\frac{3}{10}$
$\frac{2}{5}$

The value of E(X2) is:

  1. 3
  2. 5
  3. 7
  4. 10
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Q 5M.C.Q (1 Marks)1 Mark
A random variable X takes the values 0, 1, 2, 3 and its mean is 1.3. If P(X = 3) = 2P(X = 1) and P(X = 2) = 0.3, then P(X = 0) is:
  1. 0.1
  2. 0.2
  3. 0.3
  4. 0.4
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Q 61 Marks1 Mark
The probability distribution of random variable X is given below:

$\text{X}$
$0$
$1$
$2$
$3$
$\text{P}(\text{X})$
$\text{k}$
$\frac{\text{k}}{2}$
$\frac{\text{k}}{4}$
$\frac{\text{k}}{8}$

 Find $\text{P}(\text{X}\leq2)+\text{P}(\text{X}>2)$

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Q 72 Marks2 Marks
The probability distribution function oif a random variable X is given by

Xi 0 1 2
Pi 3c3 4c - 10c2 5c - 1

Where c > 0

Find: P(X < 2).

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Q 82 Marks2 Marks
The probability distribution function oif a random variable X is given by

Xi 0 1 2
Pi 3c3 4c - 10c2 5c - 1

Where c > 0

Find: c.

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Q 92 Marks2 Marks
The probability distribution of random variable X is given below:

$\text{X}$
$0$
$1$
$2$
$3$
$\text{P}(\text{X})$
$\text{k}$
$\frac{\text{k}}{2}$
$\frac{\text{k}}{4}$
$\frac{\text{k}}{8}$

 Determine $\text{P}(\text{X}\leq2)$ and $\text{P}(\text{X}>2)$

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Q 102 Marks2 Marks
The probability distribution of random variable X is given below:

$\text{X}$
$0$
$1$
$2$
$3$
$\text{P}(\text{X})$
$\text{k}$
$\frac{\text{k}}{2}$
$\frac{\text{k}}{4}$
$\frac{\text{k}}{8}$

 Determine the value of k.

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Q 112 Marks2 Marks
The probability distribution function oif a random variable X is given by

Xi 0 1 2
Pi 3c3 4c - 10c2 5c - 1

Where c > 0

Find: $\text{P}(1<\text{X}\leq2)$

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Q 123 Marks3 Marks
Find the mean and standard deviation of the following probability distributions:
$\text{x}_\text{i}$
$0$
$1$
$2$
$3$
$4$
$5$
$\text{p}_\text{i}$
$\frac{1}{6}$
$\frac{5}{18}$
$\frac{2}{9}$
$\frac{1}{6}$
$\frac{1}{9}$
$\frac{1}{18}$
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Q 133 Marks3 Marks
Find the mean and standard deviation of the following probability distributions:
xi -2 -1 0 1 2
pi 0.1 0.2 0.4 0.2 0.1
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Q 143 Marks3 Marks
Find the mean and standard deviation of the following probability distributions:
$\text{x}_\text{i}$
$-5$
$-4$
$1$
$2$
$\text{p}_\text{i}$
$\frac{1}{4}$
$\frac{1}{8}$
$\frac{1}{2}$
$\frac{1}{8}$
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Q 153 Marks3 Marks
Find the mean and standard deviation of the following probability distributions:
xi -3 -1 0 1 3
pi 0.05 0.45 0.20 0.25 0.05
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Q 163 Marks3 Marks
Find the mean and standard deviation of the following probability distributions:
xi -1 0 1 2 3
pi 0.3 0.1 0.1 0.3 0.2
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Q 174 Marks4 Marks
A class has 15 students whose ages are 14, 17, 15, 14, 21, 19, 20, 16, 18, 17, 20, 17, 16, 19 and 20 years respectively. One student is selected in such a manner that each has the same chance to being selected and the age X of the selected student is recorded. What is the probability distribution of the random variable X.
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Q 184 Marks4 Marks
Let X denot the number of colleges where you will apply after your results and P(X = x) denotes your probability of getting admission in x number of colleges. It is given that
$\text{P}(\text{X = x})=\begin{cases}\text{kx},&\text{if}\text{ x}=0\text{ or }1\\2\text{kx},&\text{if x = 2}\\\text{k}(5-\text{x}),&\text{if x = 3 or 4}\\0,&\text{if x > 4}\end{cases}$
where k is a positive constant. Find the value of k. Also find the probability that you will get addmission in
  1. Exactly one college.
  2. At most two colleges.
  3. At least two colleges.
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Q 194 Marks4 Marks
A fair die is tossed. Let X denote 1 or 3 according as an odd or an even number appears. Find the probability distribution, mean and variance of X.
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Q 204 Marks4 Marks
A fair coin is tossed four times. Let X denote the number of heads occuring. Find the probability distribution, mean and variance of X.
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Q 214 Marks4 Marks
Two cards are drawn simultaneously from a pack of 52 cards. Compute the mean and standard deviation of the number of kings.
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