4. Determine the probability density function for each of the following cumulative distribution functions. x< 0 0.2x Osx< 4 F(x) = 0.04x + 0.64 4sx< 9 1
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- Verify that p(x) = 3x−4 is a probability density function on [1,∞) and calculate its mean value.If X is a continuous variable in the range 3 > X > 0 and its distribution function is as follows: F ( x ) = k : ( x3 + x2) find the probability density function?Verify that p(x) = 3x - 4 is a probability density function on [1, oo)and calculate its mean value.
- Suppose that the probability density function of x is fx=3x2, 0<x<1 0, elsewhere Determine p(x < (1/3)), p((1/3) ≤ x < (2/3)), and p(x ≥ (2/3)) Determine the cumulative distribution function of x.The time, X, to infection for Eagle Flu in minutes, after coming into contact with the virus has cumulative distribution F with the following definition:F(x) = 0 for x < 1 and F(x)= (3/2)-(3/2x) for 0 ≤ x ≤ 3 a) What is the probability density function for X for 1 ≤ x ≤ 3? f(x) = .5 f(x) = (3/4x^2) f(x) =(3/2x^2) f(x) = (3/2)-(3/2x) f(x) = (3x/2x^3) b) What is the probability that X > 2? c) What is the probability X < 2 ? d) What is the probability that X > 2.5? e) What is the probability that X > 3? f) What is the probability that X > 2.5 given the X > 2? g) Calculate the 60th percentile of X. h) What is the expected value of X? i) What is the expected value of X2 j) What is the variance of X? k) What is the probability that X is more than 0.1 above its expected value?Suppose that X and Y have a joint probability density function given by
- Which of the following tables shows a valid probability density function? Select all correct answers. Select all that apply: x P(X=x) 0 14 1 38 2 38 x P(X=x) 0 18 1 18 2 34 x P(X=x) 0 −310 1 110 2 15 3 1 x P(X=x) 0 0.74 1 0.0 2 0.54 x P(X=x) 0 110 1 15 2 35 x P(X=x) 0 0.18 1 0.76 2 0.0Sketch the graph of the probability density function over the indicated interval. F(x) = 5/4(x+1)^2', [0, 4] Find the indicated probabilities. a) P(0 < x < 2) b) P(2 < x < 4) c) P(1 < x < 3) d) P(x ≤ 3)