A random Variable X has a probability Density function. [(π/16) cos(π x/8) 4 ≤ x ≤4 elsewhere fx(x) = {(π Find: - (a) (b) (c) Its mean X Its second moments X² or m₂ Its variance or var (X) or o
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- 6. Use the moment-generating function of gamma distribution to show that E(X)=a0 and Var (X)=a0²If X has probability density function f(x) = X/32 on [0, 8], find the expected value and the standard deviation of X. Give your answer either as a irreducible fraction or a decimal number accurate to 2 decimal places. E(X) = std(X) =For what value of c is the function f(x) = {c/x³ if x ≥ 1 {gx3 otherwise a probability density function?
- Q2. The probability density function of X is as follows. f(x) = 2 - 2x, for x = [0, 1] Which one of the following expressions can be used to find P(0.5 < X < 1.5)? F(x) is the cumulative distribution function of X. (A) 1 - F(0.5) (C) F (1.5)-f(0.5) (B) f(1.5)-f(0.5) (D) 1.5 (2 - 2x) dx (E) other[2] X is an exponential random variable with variance 9. If (X, Y = (2, otherwise, 1Q6. A continuous random variable has probability density function = { / (2x - 3) ,15x52 0 , otherwise f(x) = The find the value of P(1.5 ≤ x ≤ 4)The continuous random variable X has the following probability density function (pdf), for some positive constant c, for 0 < x < c. 3 (1+x)³ f(x)= (a). Prove that c= √3-1. (a) Accept c = √√3-1. Plot f(x) in the range. (b) Find E(X); Var (X) using numerical integration. (c) Use Inversion method, find 20 random numbers from X =Q1:Let X be a random variable with pdf f (x) = cx + d for 0 = a- Find the values of constants c and d. b- Find the cdf of X. c- find P(IX| <). P([1] The probability density function of a random variable X is SC(x + 4), -4 4.Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,