Probability (Probability Distribution and Binomial Distribution) Previous Years Board Questions with Solutions-ISC-Class 12-Mathematics

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Random variable: Let S be the sample space associated with a given random experiment.

Then, a real-valued function X which assigns a unique real number X(w) to each w ∈ S, is called a random variable.

A random variable that can assume only a finite number of values is called a discrete random variable.

Probability distribution: If a random variable X takes values $x_{1},\, x_{2},\, ....\, ,\, x_{n}$ with respective probabilities $p_{1},\, p_{2},\,.....\, p_{n},$ then,

$X:\, \,\: \: x_{1}\: \:\:\: x_{2}\: \:\: \: x_{3}\: \: \: \: ...\: \: \: \: x_{n}$

$P(X):\: \: \: p_{1}\: \: \: \: p_{2}\: \: \: \: p_{3}\: \: \: \: ...\: \: \: \: p_{n}$

is known as the probability distribution of X.

Mean: $\mu =\sum_{i=1}^{n}x_{i}p_{i}$

Variance: $\sigma ^{2}=(\sum x_{i}^{2}p_{i}-\mu ^{2})$

Standard deviation: $\sigma =\sqrt{var iance}$

S Probability distribution 1 S Probability distribution 2 S Probability distribution 3 S Probability distribution 4 S Probability distribution 5 S Probability distribution 6 S Probability distribution 7 S Probability distribution 8

ISC Class 12 Mathematics

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Matrices (2000 to 2020)	Matrices (2000 to 2020)
Determinants (2000 to 2020)	Determinants (2000 to 2020)
Differentiation (2000 to 2020)	Differentiation (2000 to 2020)
Rolle’s Theorem and Lagrange’s Mean Value Theorem (1998 to 2020)	Rolle’s Theorem and Lagrange’s Mean Value Theorems (1998 to 2020)
Maxima and Minima (2000 to 2020)	Maxima and Minima (2000 to 2020)
Integration (1990 – 2011)	Integration (1990 – 2011)
Integration (2012 to 2020)	Integration (2012 to 2020)
Differential Equations (1991 to 2005)	Differential Equations (1991 to 2005)

Differential Equations (2006 to 2020)	Differential Equations (2006 to 2020)
Probability (Addition and Multiplication Theorem-Conditional Probability) (1993 to 2020)	Probability (Addition and Multiplication Theorem, Conditional Probability) (1993 to 2020)
Probability (Baye’s Theorem) (2000 to 2019)	Probability (Baye’s Theorem) (2000 to 2019)
Probability (Probability distribution and Binomial distribution) (1992 to 2020)	Probability (Probability distribution and Binomial distribution) (1992 to 2020)
Application of Calculus in Commerce and Economics (2005 to 2020)	Application of Calculus in Commerce and Economics (2005 to 2020)
Linear Programming (2008 to 2020)	Linear Programming (2008 to 2020)
Linear Regression (2005 to 2020)