xample: A continuous random Variable x has X70 fx(x)= 120 0 Find the E(X). -ax X40 probability density given by [6] 1
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![Example: A continuous random Variable x has
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X70
£260
0
Find the E(X).
fx (x)=
-ax
X40
probability density given by
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- (****) A continuous random variable X has probability density function (PDF) for some constants a and b. If Pr(X ≤ 0) is 2 times Pr(X > 0), what are a and b? a= b = f(x) = Jae for x < 0 (bxe-x² for x ≥ 0Verify Cauchy - Schwarz's inequality (cosine inequality) for random variables stated as [E (XY)P SE (X?) · E (Y²)Let Xbe a random variable with density function (2x² - 1[Q1] The probability distribution of the discrete random variable X is: f(X) = k23-* , for x = 4,5, 6, 7 (a) Find: • the value of the constant k. • The mean E (X). • The variance Var(X). (b) Sketch F(X).A random variable has probability density function f(x) = 30x (1 - x) <(0 < xs 1). Compute its cumulative distribution F(x). O 10x3- 15x4 + 6x5 + 1 O 30x(1 - x) O 30x2 - 60x3 + 30x4 O 10x3 - 15x4 + 6x5 O none of these A Moving to the next question prevents changes to this answer. to search 63°F S End F10 Home %23 PrtScn F8 F2 F3 F4 F5 F6 F7 F9 近Let X be a random variable taking positive values and assume that E(X) exists. Which of the following statements are true? • (i) E(X*) > (E(X))*. • (ii) E(1/X²) > 1/E(X²). • (ii) E(e-3X) > e°A continuous random variable has probability density function given by K(2x-3);1<x2 Find k if f(x) is a probability density functionThe probability density function of a random variable is kx3 f(x) = if 0 < xs 2 V25 – x2 = 0 otherwise Find the k.Continuous random variables 6. A charity group raises funds by collecting waste paper. A skip-full will contain an amount, X of other materials such as plastic bags and rubber bands. X may be regarded as a random varibales with probability density funnction. All nmerical values are in units of 100kg. Find the Expected value and Standard deviation.Express your answer in 3 decimal place value f(x)= - c(x-1)(4-x) 0 for 1The probability density function of the Pareto distribution is given as: f(x) =- (x>0) (1+x)*1 Show that: Var(x) = ( α- 1), (α-2)Continuous random variables 5. A charity group raises funds by collecting waste paper. A skip-full will contain an amount, X of other materials such as plastic bags and rubber bands. X may be regarded as a random varibales with probability density funnction. All nmerical values are in units of 100kg. Calculate c. express your answer in fraction c(x - 1)(4x) f(x) = _{[C(x − 1) for 1Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON