1.The probability density function of a continuous random variable X is given by f(x) : 04 i) Find k ii) Find P (1.5
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Q: X is continuous random variable with probability density function px +1,0 k) =
A: (a) Here, Hence the value of p is -1. Since we can calculate q as follows: Hence the value of…
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Q: 19 a) Find the probability that X > 0.5 0.4753 b) Find the probability that 0.3 < X < 0.63 0.3423 c)…
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Q: Q2 The probability density function for the continuous random variable X is given by: (A(x² – 2x +…
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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: NeitherQ1. The cumulative distribution function of the random variable X is F(x) = 0, (x+1)², 1- (1-2)², 1, for x 1 (a) Compute-P(0.5 < X <1)¶ (b) What is the probability density function of X.?Given 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)1/3
- The probability density function (p.d.f.) of a continuous random variable X is defined to be: kx + for 0 < x < 1 f(x) = |0 otherwise, for some constant k. For these problems, please ensure your answers are accurate to within 3 decimals. Part a) Find the value of k that makes the above function a proper p.d.f. Part b) Find E(X).49 -Probability density function for a continuous random number For 1 <x <3, it is equal to f (x) = (6/32) x +2/16. for other cases, f (x) = 0. Find the cumulative probability function F (x <1 and x = 1) of the continuous probability division. A)1/5 B)0 C)1/2 D)1/4 TO)3/4
- Let 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 XA continuous random variable, X, has the following probability density function. k cos for 0sxs1 f(x)=- for all other values of x (a) Show that k = Find p( x sxs). (b) (c) Find the median of X.|A 9 a) The continuous random variable Xhas probability density function f (x) = 0(1– x)"-1 , 0 0 i) Find the cumulative distribution function, F(x), of X ii) Find P(0.251. 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.Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON