Topics
Mathematical Logic
- Statements and Truth Values in Mathematical Logic
- Logical Connectives
- Tautology, Contradiction, and Contingency
- Quantifier, Quantified and Duality Statements in Logic
- Negations of Compound Statements
- Converse, Inverse, and Contrapositive
- Algebra of Statements
- Application of Logic to Switching Circuits
- Overview of Mathematical Logic
Matrices
Trigonometric Functions
Pair of Straight Lines
Vectors
Line and Plane
Linear Programming
Differentiation
- Introduction & Derivatives of Some Standard Functions
- Derivative of Composite Functions
- Geometrical Meaning of Derivative
- Derivative of Inverse Function
- Logarithmic Differentiation
- Derivatives of Implicit Functions
- Derivatives of Parametric Functions
- Higher Order Derivatives
- Overview of Differentiation
Applications of Derivatives
- Applications of Derivatives in Geometry
- Derivatives as a Rate Measure
- Approximations
- Rolle's Theorem
- Lagrange's Mean Value Theorem (LMVT)
- Increasing and Decreasing Functions
- Maxima and Minima
- Overview of Applications of Derivatives
Indefinite Integration
Definite Integration
- Definite Integral as Limit of Sum
- Integral Calculus
- Methods of Evaluation and Properties of Definite Integral
- Overview of Definite Integration
Application of Definite Integration
- Application of Definite Integration
- Area Bounded by Two Curves
- Overview of Application of Definite Integration
Differential Equations
Probability Distributions
- Random Variables
- Probability Distribution of Discrete Random Variables
- Probability Distribution of a Continuous Random Variable
- Variance of a Random Variable
- Expected Value and Variance of a Random Variable
- Overview of Probability Distributions
Binomial Distribution
Estimated time: 4 minutes
- Apply arithmetic mean of frequency distribution to find the expected value of a random variable
- Calculate the Variance and S.D. of a random variable
Maharashtra State Board: Class 12
Definition: Expected Value
If a discrete random variable X has possible values x₁, x₂, …, xₙ with corresponding probabilities p₁, p₂, …, pₙ, then the expected value E(X) is defined as
E(X) = x₁p₁ + x₂p₂ + … + xₙpₙ = Σ xᵢpᵢ
E(X) is also called the mean, which is denoted by μ.
Maharashtra State Board: Class 12
Formula: Expected Value
E(X) = Σxᵢpᵢ
Maharashtra State Board: Class 12
Formula: Variance
Var = E(X²) − [E(X)]²
Maharashtra State Board: Class 12
Formula: Standard Deviation
\[\mathrm{SD}(X)=\sqrt{E(X^{2})-\left[E(X)\right]^{2}}\]
SD = √Var
Related QuestionsVIEW ALL [9]
Find the expected value, variance and standard deviation of random variable X whose probability mass function (p.m.f.) is given below:
| X = x | 1 | 2 | 3 |
| P(X) | `1/5` | `2/5` | `2/5` |
The probability distribution of X, the number of defects per 10 metres of a fabric is given by
| x | 0 | 1 | 2 | 3 | 4 |
| P(X = x) | 0.45 | 0.35 | 0.15 | 0.03 | 0.02 |
Find the variance of X
