Preparing for the IIT JAM Statistics exam requires strong understanding of formulas and concepts. Many questions in the exam are based directly on statistical formulas. Because of this, students should revise important formulas regularly.

An IIT JAM Statistics formula sheet helps students remember important formulas and revise topics quickly before the exam. Instead of searching formulas in many books, students can use a single formula sheet for fast revision.

In this guide, we will cover important formulas from major topics such as probability, random variables, distributions, statistical inference, linear algebra, and calculus.

Probability Formulas

Probability is one of the most important topics in the IIT JAM Statistics exam. It measures the likelihood that an event will occur.

The basic probability formula is:

P(A) = \frac{n(A)}{n(S)}

Where:

• $P(A)$P(A) = probability of event A
• $n(A)$n(A) = number of favorable outcomes
• $n(S)$n(S) = total number of outcomes

Important probability rules include:

Addition Rule

If A and B are events:$$P(A \cup B) = P(A) + P(B) – P(A \cap B)$$P(A∪B)=P(A)+P(B)−P(A∩B)

Conditional Probability$$P(A|B) = \frac{P(A \cap B)}{P(B)}$$P(A∣B)=P(B)P(A∩B)​

These formulas help calculate probability when multiple events are involved.

---

Random Variable Formulas

A random variable represents the numerical result of a random experiment.

Expected Value

The expected value of a random variable is the average outcome.$$E(X) = \sum xP(x)$$E(X)=∑xP(x)

Variance

Variance measures how much the values spread around the mean.

\sigma^2 = \frac{1}{N}\sum_{i=1}^{N}(x_i – \mu)^2

Where:

• $\mu$μ is the mean
• $N$N is the number of observations

Standard deviation is the square root of variance.

---

Binomial Distribution Formulas

Binomial distribution is used when an experiment has two possible outcomes.

The probability mass function is:$$P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$$P(X=k)=(kn​)pk(1−p)n−k

Important properties:

Mean:$$E(X) = np$$E(X)=np

Variance:$$Var(X) = np(1-p)$$Var(X)=np(1−p)

---

Poisson Distribution Formulas

Poisson distribution is used when events occur independently over a fixed interval.

Probability function:$$P(X = k) = \frac{e^{-\lambda} \lambda^k}{k!}$$P(X=k)=k!e−λλk​

Mean and variance are both equal to $\lambda$λ.

---

Normal Distribution Formula

Normal distribution is one of the most widely used probability distributions.

Probability density function:$$f(x) = \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}$$f(x)=σ2π​1​e−2σ2(x−μ)2​

Where:

• $\mu$μ = mean
• $\sigma$σ = standard deviation

---

Standard Normal Distribution

A standard normal variable is obtained using the Z-score formula.

$z = \frac{x – \mu}{\sigma}$z=σx−μ​

$x$x

$\mu$μ

$\sigma$σ

$z=\frac{x-\mu}{\sigma}\approx 1.2$z=σx−μ​≈1.2

$\Phi(z)\approx 88.5\%$Φ(z)≈88.5%

This formula converts any normal variable into a standard normal variable.

---

Sampling Distribution Formulas

Sampling distribution describes the distribution of a statistic calculated from a sample.

Mean of sample mean:$$E(\bar{X}) = \mu$$E(Xˉ)=μ

Variance of sample mean:$$Var(\bar{X}) = \frac{\sigma^2}{n}$$Var(Xˉ)=nσ2​

Where:

• $n$n is the sample size.

---

Hypothesis Testing Formulas

Hypothesis testing helps determine whether a statistical assumption is correct.

Test statistic:$$Z = \frac{\bar{X} – \mu}{\sigma/\sqrt{n}}$$Z=σ/n​Xˉ−μ​

Students use this formula to compare sample results with population parameters.

---

Linear Algebra Formulas

Linear algebra is another important part of the IIT JAM syllabus.

Determinant of 2×2 Matrix$$|A| = \begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad – bc$$∣A∣=​ac​bd​​=ad−bc

Matrix Multiplication

If $A$A is $m \times n$m×n and $B$B is $n \times p$n×p, then:$$AB$$AB

will be $m \times p$m×p.

---

Eigenvalues and Eigenvectors

Eigenvalues satisfy the equation:$$|A – \lambda I| = 0$$∣A−λI∣=0

Where:

• $A$A is a matrix
• $I$I is the identity matrix
• $\lambda$λ represents eigenvalues.

---

Calculus Formulas

Calculus formulas are useful in probability and optimization problems.

Derivative$$\frac{d}{dx} (x^n) = nx^{n-1}$$dxd​(xn)=nxn−1

Integral$$\int x^n dx = \frac{x^{n+1}}{n+1} + C$$∫xndx=n+1xn+1​+C

---

Tips to Use the IIT JAM Statistics Formula Sheet

Students should use the formula sheet regularly during preparation.

Helpful tips include:

• Revise formulas daily
• Write formulas in short notes
• Practice problems using formulas
• Review formulas before mock tests

Regular revision helps students remember formulas during the exam.

---

Why Formula Sheets are Important for IIT JAM

Formula sheets are very useful for quick revision.

Benefits include:

• Saves time during revision
• Helps remember important formulas
• Makes exam preparation more organized
• Reduces confusion during the exam

Many students revise formulas from a single sheet before entering the exam hall.

---

Conclusion

Preparing for the IIT JAM Statistics exam requires strong understanding of formulas and concepts. Students should revise probability, distributions, hypothesis testing, linear algebra, and calculus formulas regularly.

Using a well-organized IIT JAM Statistics formula sheet can make revision easier and improve confidence before the exam.

With consistent practice and regular revision of formulas, students can perform better in the IIT JAM Statistics exam.