Download App

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

Uttarakhand Board (UBSE) - STD 12 Science - Maths (Uttarakhand - 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
Question types
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:
$\text{X}:$
$1$
$2$
$3$
$4$
$\text{P}(\text{X}):$
$\frac{1}{10}$
$\frac{1}{5}$
$\frac{3}{10}$
$\frac{2}{5}$
The value of $E(X^2)$ is:
  • A
    $3$
  • B
    $5$
  • C
    $7$
  • ✓
    $10$

Answer: D.

View full solution →
Q 2M.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:
  • A
    8
  • B
    16
  • ✓
    32
  • D
    48

Answer: C.

View full solution →
Q 3M.C.Q (1 Marks)1 Mark
Let $X$ be a discrete random variable. Then the variance of $X$ is:
  • A
    $E(X^2)$
  • B
    $E(X^2) + (E(X))^2$
  • ✓
    $E(X^2) - (E(X))^2$
  • D
    $\sqrt{\text{E}(\text{X}^2)-(\text{E}(\text{X}))^2}$

Answer: C.

View full solution →
Q 5M.C.Q (1 Marks)1 Mark
If $X$ is a random variable with probability distribution as given below :
$X = x_i$ $0$ $1$ $2$ $3$
$P(X = X_i)$ $k$ $3k$ $3k$ $k$
The value of $k$ and its variance are :
  • A
    $\frac{1}{8},\frac{22}{27}$
  • B
    $\frac{1}{8},\frac{23}{27}$
  • C
    $\frac{1}{8},\frac{24}{27}$
  • ✓
    $\frac{1}{8},\frac{3}{4}$

Answer: D.

View full solution →
Q 61 Marks Question1 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 $\text{P}(\text{X}\leq2)+\text{P}(\text{X}>2)$
View full solution →
Q 82 Marks Questions2 Marks
A random variable X has the following probability distribution:
Values of X: 0 1 2 3 4 5 6 7 8
P(X) a 3a 5a 7a 9a 11a 13a 15a 17a
Determine:
The Value of a.
View full solution →
Q 102 Marks Questions2 Marks
Find the mean of the following probability distribution:
$\text{X}=\text{x}_\text{i}:$ $1$ $2$ $3$
$\text{P}(\text{X}=\text{x}_\text{i}):$ $\frac{1}{4}$ $\frac{1}{8}$ $\frac{5}{8}$
View full solution →
Q 123 Marks Question3 Marks
A random variable X has the following probability distribution:
Values of X: 0 1 2 3 4 5 6 7 8
P(X) a 3a 5a 7a 9a 11a 13a 15a 17a
Determine:
$\text{P}(\text{X}<3),\text{P}(\text{X}\geq3),\text{P}(0<\text{X}<5).$
View full solution →
Q 143 Marks Question3 Marks
Find the mean and standard deviation of the following probability distributions:
$\text{x}_\text{i}$
$0$
$1$
$2$
$3$
$4$
$5$
$\text{p}_\text{i}$
$\frac{1}{6}$
$\frac{5}{18}$
$\frac{2}{9}$
$\frac{1}{6}$
$\frac{1}{9}$
$\frac{1}{18}$
View full solution →
Q 153 Marks Question3 Marks
Two cards are drawn successively without replacement from well shuffled pack of 52 cards. Find the probability distribution of the number of aces.
View full solution →
Q 163 Marks Question3 Marks
An urn contain 5 red and 2 black balls. Two balls rendomly selected. Let X represent the number of black ball. What are the possible values of X. Is X a random variable?
View full solution →
Q 175 Marks Questions5 Marks
Two cards are selected at random from a box which contains five cards numbered 1, 1, 2, 2, and 3. Let X denote the sum and Y the maximum of the two numbers drawn. Find the probability distribution, mean and variance of X and Y.
View full solution →
Q 185 Marks Questions5 Marks
Two numbers are selected at random (without replacement) from positive integers 2, 3, 4, 5, 6 and 7. Let X denote the larger of the two numbers obtained. Find the mean and variance of the probability distribution of X.
View full solution →
Q 195 Marks Questions5 Marks
In a game, a man wins Rs 5 for getting a number greater than 4 and loses Rs 1 otherwise, when a fair die is thrown. The man decided to thrown a die thrice but to quit as and when he gets a number greater then 4. Find the expected value of the amount he wins or loses.
View full solution →
Q 205 Marks Questions5 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.
View full solution →
Q 215 Marks Questions5 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.
View full solution →
Browse all question groups ↑

Generate a Mean and variance of a random variable paper free

Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.

Download App
Generate Paper FreeAll Maths chapters