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- Which of the following functions are allowable as a probability density function for some continuous random variable? 0 A B D E F A: f₁(x) = C: f3(x) = {8² √3x² −1≤x≤0 else 10 I² x > 10 x < 10 E: f5(x) = 1- B: f₂(x) = D: f4(x) = x² −1 < x < 1 else {50 [5(1-x²)4 0≤x≤ 1 else (8x² - 6x +1) 0≤x≤1 else F: NeitherGiven that the probability density function of the continuous random variable X is given as follows, what is E (6X + 3X²) equal to? f(x)={ 2(1-x), 0<x<1 0, e.w a)15/18 b)5/2 c)1/18 d)1/3If X is a continuous random variable with probability density function f(x)={x, if 0<x≤√2,otherwise x=0. then E(X)= (provide an exact answer) and Var(X)= (provide an exact answer).
- Suppose an industry produced a particular type of metal mixture up to 1 ton a day. Due to technical difficulties or system breakdowns, the actual amount produced by the industry is Y, a random variable which has the following Probability density function: f(y) = √2y 0Delta Airlines quotes a flight time of 2 hours, 3 minutes for a particular flight. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 12 minutes. (a) Show the graph of the probability density function for flight time. f(x) f(x) esc 4 116 1-12 f(x) 4 116 1 114 126 120 Flight Time in Minutes 19 # 00 $ 132 X i DIT % 116 1-12 114 ♫ 120 126 Flight Time in Minutes MA A 4 Seungr & 132 W D X P f(x) 1|4 6 1-12 114 120 126 Flight Time in Minutes 国人 cricut ||| T 132 X + OLet XE {-1,0, 1} . That is, X is a discrete random variable only takes three values -1, 0, and 1. Suppose the equality for Chebyshev's inequality holds for X and P(X = 0) = 0.3 , find P(X = 1) Let X be a random variable with probability density f(x) = x6 for x > 1 and O else. Use Chebyshev's inequality to bound P(X > 2.5) . Round your answer to 3 decimal places.Let X be a continuous random variable with cdf F(x). Show that E(I(X < x)) = F(r) where I is the indicator function (1 if XIf 'X' is a continuous random variable, then the expected value is given by O a. SXP(X) O b. P(X) O C. No value such as expected value d. [x P(x) م1. Consider a random variable X with probability density function given as: 0 if x < 0, 1 if 0 ≤ x ≤ 1, f(x) 2 1 if 1 < <∞. -2x² Verify if f(x) is indeed a density function. If it is, find the distribution function of X.Suppose that the probability density function of a random variable X is as follows: f(x)= cx, for0<x<4; 0, otherwise. (a) Find c.(b) Find the cumulative distribution function F and sketch it.Let X be a continuous random variable with p.d.f. f(x) and distribution function F(x). If Y = X², (a) what is the g(y)? 14/12 (b) If ƒ(x) = -√2/² 2π -∞Recommended 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