List of top Engineering Mathematics Questions on Probability

In a Poisson distribution, \[ P(X=x+k)=\frac{\lambda^k}{f(x)}P(X=x), \] then \(f(x)=\)

If \[ \frac{dy}{dx}=xy+x,\; x\in\mathbb{R} \] and \(y(0)=1\), then \(y(0.2)\) with step size \(h=0.1\) using Euler's method is

A random variable \(X\) has the probability density function \[ f(x)=Kx,\qquad 0\lt x\lt 2, \] then the ratio between \(K\) and the mean of \(X\) is

If \(A\) and \(B\) are independent random variables, then which of the following is correct?

Consider the differential equation \[ \frac{dy}{dx}=x^{2}-y,\qquad y(0)=1. \] Using the Simple Euler's Method with a step size of \(h=0.1\), the value of \(y(0.1)\) is

Assertion (A): If \(X\sim N(\mu,\sigma^{2})\), then \[ P(X<\mu)=0.5. \] Reason (R): Normal distribution is symmetric about its mean.

If $X \sim N(\mu,\sigma^2)$ then:

Assertion (A): Spearman rank correlation coefficient is used for ordinal data.
Reason (R): It is based on ranks rather than actual values.

Consider the differential equation \[ \frac{dy}{dx}=x^{2}-y,\qquad y(0)=1. \] Using the Simple Euler's Method with a step size of \(h=0.1\), the value of \(y(0.1)\) is

Assertion (A): If \(X\sim N(\mu,\sigma^{2})\), then \[ P(X<\mu)=0.5. \] Reason (R): Normal distribution is symmetric about its mean.

While evaluating \(\int_{a}^{b} f(x) \, dx\) using Trapezoidal rule and Simpson's one-third rule, \([a,b]\) is divided into n number of subintervals so that both the methods can be applied for the same division, then a possible value of n is

Newton-Raphson method is used to find the root of \(x^2 - 3 = 0\). If the initial solution is taken as \(x = -2\), then the iterations tend to