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Consider a random process given by x(t) = A cos (2π fC t + θ), where A is a Rayleigh distributed random variable and θ is uniformly distributed in [0, 2π]. A and θ are independent. For any time t, the probability density function (PDF) of x(t) is:
A random process is defined by X(t) + A where A is continuous random variable uniformly distributed on (0,1). The auto correlation function and mean of the process is
Consider the continuous random variable with probability density function
f(t) = 1 + t for -1 ≤ t ≤ 0
      = 1 - t for 0 ≤ t ≤ 1
The standard deviation of the random variable is
It is assumed that quantization error, e(n) is a sequence of random variables where 1. The statistics do not change with time. 2. It is a sequence of uncorrelated random variables. 3. It is uncorrelated with the quantizer input x(n). 4. The probability density function is uniformly distributed over the range of values of quantization error. Which of the above statements are correct?
An object X sinks in liquids P and Q but floats in liquid R. Which of the following conclusions can be made from these observations? A) Density of X is more than the density of P B) Density of X is less than the density of R C) Density of P is equal to the density of R D) Density of P is less than the density of R
What is linear_congruential_engine? for some w using Mersenne Twister algorithm b) Pseudo-random number engine that generates random unsigned integers c) Pseudo-random number engine that generates random unsigned integers in the range for some w using lagged Fibonacci generator d) Pseudo-random number engine that generates random signed integers in the range for some w using Mersenne Twister algorithm
If {x} is a continuous, real valued random variable defined over the interval (-$$\infty $$, +$$\infty $$) and its occurrence is defined by the density function given as:
$${\text{f}}\left( {\text{x}} \right) = \frac{1}{{\sqrt {2\pi } * {\text{b}}}}{{\text{e}}^{\frac{{ - 1}}{2}{{\left( {\frac{{{\text{x}} - {\text{a}}}}{{\text{b}}}} \right)}^2}}}$$     where 'a' and 'b' are the statistical attributes of the random variable {x}. The value of the integral $$\int_{ - \infty }^{\text{a}} {\frac{1}{{\sqrt {2\pi } * {\text{b}}}}{{\text{e}}^{\frac{{ - 1}}{2}{{\left( {\frac{{{\text{x}} - {\text{a}}}}{{\text{b}}}} \right)}^2}}}{\text{dx}}} $$
The graph of a function f(x) is shown in the figure.
Probability and Statistics mcq question image
For f(x) to be valid probability density function, the value of h is
Let f(x) be the continuous probability density function of a random variable X. The probability that a
Statement I The product of coefficient of correlation, standard deviation of variable 'X' and Standard deviation of variable 'Y' gives the measure of covariance between X and Y variables.
Statement II The product of coefficient of correlation between X and Y variables and the ratio between standard deviation of X variable to standard deviation of Y variable measures the slope of the regression line of X on Y variable.