A sample of women's heights was taken. Their heights (in inches) are defined by the following probability function. 0.0825x -5.0325 f(x) = -0.0425x + 2.9325 0 for 61 < x < 65 for 65 ≤ x < 69 elsewhere The graph of f(x), the density curve, is shown below. 0.35 0.30 0.25 0.20 0.15 Density
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- Sketch the graph of the probability density function over the indicated interval and find the indicated probabilities. f(x)= (3/16 √x) [0,4] A)P(0<x<2)B)P(2<x<4)C)p(1<x<3)D)P(x≤3)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?Verify that p(x) = 3x−4 is a probability density function on [1,∞) and calculate its mean value.
- suppose x has an exponential distribution with probability density function f(x) =2e^-2x, x>0. Then P(X>1)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?An insurance company provides customers with both auto and home insurance policies. For a particular customer, Χ is the deduction on his or her auto policy and Y is the deduction on the home policy. Possible values of Χ are K100 and K250, and for Y are K0, K100 and K200. The joint probability density function for (Χ,Y ) is given by the following table: X Y K100 K250 K0 0.20 0.05 K100 0.10 0.15 K200 0.20 0.30 Find the probability for a randomly selected policy holder having a K100 deduction on the auto insurance and a K200 deduction on the home insurance. Find the probability that a randomly selected policy holder has a home deduction of at least K100. Are the random variables Χ and Y independent? Explain your answer. If we look only at those insurance customers selecting the lowest auto mobile insurance deduction (K100), what is the probability that a randomly selected…
- 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.Determine the conditional probability distribution of Y given that X = 1. Where the jointprobability density function is given by f(x,y)=1/64xy for 0 < x < 4 and 0 < y < 4.Suppose that random variable X is uniformly distributed between 6 and 28. Draw a graph of the density function, and then use it to help find the following probabilities: A. P (X > 28) = B. P(X < 11.5) = C. P(9 < X < 26) = D. P(13 < X < 30) =