Problem #1: Let X~ Unif[-2, 2], and Y = (X+ 1)². Problem #1(a): Problem #1(b): (a) Find fy() and fy(4), where fy() is the probability density function of Y. Separate your answers with a comma. (b) Find P{Y < 4}. Enter your answer symbolically, as in these examples Enter your answer symbolically, as in these examples
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.Repeat Example 1a for the function f(x)=2x2 on [1,2]. What is the probability that X will be between 32 and 2?9) The effectiveness of solar-energy heating units depends on the amount of radiation available from the sun. During a typical October, daily total solar radiation in Tampa, Florida, approximately follows the following probability density function (units are in hundreds of calories): 3 f (x) ={32 (x- 2)(6-x) for23. Show that the following are probability density functions: 1 (a) f(x) = -2*, x = 1, 2, ..., N, and zero elsewhere 2N+1-2 (b) f(x)=p(1-p)*, x=0, 1, 2, ..., and zero elsewhere; 01. Suppose X has probability function f(x)= x/6 x=1, 2, 3 Find g(y) if Y=X²(1) Let X b(16,- 5,-) find E(4- 3x) and distribution function.Example 2.17 Let X be a continuous type random variable with PDF given as 1 = (x)f 27 Let Y be another random variable such that Y = X². Find the PDF of Y.Problems 4.2. Suppose that X is a continuous random variable with probability density function given by f(x) = x² + x + } for 0Please help me with this problem. ASAP! within 2hours. Show complete and explicit step and don't skip any mathematical solution. Consider a probability density function (PDF), where f(T-t) is a general function, g(T) and h(t) are time-dependent functions. (a) Calculate the first moment of the PDF. (b) Calculate the second moment of the PDF. (c) Calculate the variance.Recommended textbooks for youAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,