Consider a continuous random variable X with pdf f,(x) and moment generating function M,(v), then Chernoff's inequality states that P{X >a} 0
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- Let X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.Find the mean of random variable of X, if X is random variable with pdf f(x) = c(1-x²), -1Suppose X is a random variable, whose pdf is defined as follows: 2x = (²x) (u(x) - u(x − 3)) where u(x) is the unit step function. Determine the conditional pdf fx(x 1Let the random variable X be the time in seconds between incoming telephone calls at a busy switchboard. Suppose that a reasonable probability model for X is given by the pdf: fx(x) = { ie for 0Let X be a random variable with pdf: f(x)= k(10 - 2x) for x being [0,5] a.) Find k b.) Find E(X) c.) Find Var(X) d.) Find E(3 *squareroot(X))B) Let the random variable X have the moment generating function e3t M(t) for -1A gasoline station gets its supply once a week. Suppose the PDF of X = demand in thousands of gallons for gasoline is: fx(x) = 5(1 – x)*I(0.1)(x) a. What is the probability that the demand for gasoline in a given week is more than 500 gallons? b. How much gasoline must the station get from its supplier in order for the probability that its supply will be exhausted in a given week shall be 0.01?Let X be a random variable with pdf f(x) = kx*,-1Suppose that X1 and X2 are independent and exponentially distributed random vari- X1 Find X2 ables, both with mean Let Y1 = X1 + X2 and Y2 (a) the joint pdf of Y1 and Y2 (including its domain). (b) P[Y1 > 2|Y2 > 1].The random variable X has PDF given by 1 f(x)=√e-2/4 -x/4 for x > 0, zero otherwise. Compute P(X> 5) rounding to four decimal places.(ii) Suppose that X₁ and X₂ have joint pdf 2, 10, Compute the joint pdf of random variables Y₁ = X₁ and Y₂ = X2. f(x1, x₂): for 0 < x1 < x₂ < 1 otherwise =Let X be a random variable with discrete pdf f(x) = x/8 if x = 1, 2, 5, and zero otherwise. Find: (a) E(X).SEE MORE QUESTIONSRecommended textbooks for youCalculus 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:CengageCalculus 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:Cengage