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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

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 Correct Answer 1/3 & 1/2

E = 1/3 and E = 1/2 respectively.

Related Questions

Which of the following statements relating to correlation and reegression are true?
1. The coefficient of correlation is independent of change of origin and scale
2. The coefficient of correlation between the two variables is the arithmetic average of the two regression coefficients
3. The probable error of the coefficient correlation is 0.6745 times of its standard error
4. Coefficient of correlation multiplied by the ratio between the standard deviations of the two variables denotes the slope of the regression line
Select the correct answer:
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.
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:
Which of the following statements are true?
1. The coefficient of rank correlation has the same limits as the Karl Pearson's coefficient of correlation.
2. The coefficient of correlation is independent of the change of origin but not of scale.
3. The covariance between $$X$$ and $$Y$$ is defined as $$\frac{{\sum {xy} }}{n}$$ where, $$x = \left( {X - \overline X } \right),y = \left( {Y - \overline Y } \right)$$      and $$n = $$ no. of paired observations.
4. $${b_{xy}}$$ is called regression coefficient of $$X$$ variable on $$Y$$ variable.
5. If $${b_{xy}}$$ is 0.4 and $${b_{yx}}$$ is 1.6, coefficient of determination would be 0.8.
Select the correct answer:
Which of the following statements are true? a. The correlation coefficient is dependent on the choice of both origin and scale observations. b. The correlation coefficient is dependent on the units of measurements. c. The coefficient of correlation is the square root of the coefficient of determination. d. The zero value of the correlation coefficient cannot estimate the value of the dependent variable.
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 $$\int_{ - \infty }^{\text{a}} {\frac{1}{{\sqrt {2\pi } * {\text{b}}}}{{\text{e}}^{\frac{{ - 1}}{2}{{\left( {\frac{{{\text{x}} - {\text{a}}}}{{\text{b}}}} \right)}^2}}}{\text{dx}}} $$
Two autos start from the same stand. Auto A travels 2 km east, then turns to its right and travels further 3 km. Meanwhile auto B travels 5 km north, and then turns West and travels 3 km, then it turns to its left and travels 8 km. Where is auto B with respect to auto A?
Two autos start from the same stand. Auto A travels 2 km East, then turns to its right and travels a further 3 km. Meanwhile auto B travels 5 km North, then turns West and travels 3 km, then it turns to its left and travels 8 km. Where is auto B with respect to auto A?
Consider the following given statements about auto-transformers and choose the one which is/are correct. 1. Auto-transformers require less copper as compared to a conventional,2 winding transformer of the same capacity. 2. Auto-transformers provide isolation between the primary and secondary windings. 3. Auto- transformer has less leakage reactance as compared to the conventional, 2 winding transformer of the same capacity.
The probability density function of a continuous random variable distributed uniformly between x and y (for y > x) is