Given the function below, solve for the following: F(y) = {6-2 < y < 4 0, elsewhere a. Verify that f(x) is a density function. b. Find the cumulative distribution function. c. List the cumulative distribution function.
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- Given the function below, solve for the following:F(y) = {y/6, −2 < y < 4 0, elsewherea. Verify that f(x) is a density function. b. Find the cumulative distribution function. c. List the cumulative distribution function. d. Draw the Probability Mass Function PlotBelow is the probability density function for the distance, in inches, that a dart thrown by your professor lands from the “bullseye” of a dart board. The equation of the curve is: d(x) = 1/4 − 1/32 x a.What’s the probability that a dart will land less that 8 inches from the bullseye? b.What’s the probability that a dart will land between 2 and 4 inches from the bullseye? c.What’s the probability that a dart will land exactly 2 inches from the bullseye? Ex- plain. d.What’s the probability that a dart will land less than 6 inches away from the bullseye?The life (in years) of a laptop battery has a probability density function defined by P(x)=12e−x/2 for x in [0,∞). Find the probability that a randomly selected laptop battery will last between 2 and 5 years?
- With the known values of a = 200,000 and b = 230,000, the first equation for the probability density function for the sales price of a home is found as follows. f(x) = 1/b – a, a ≤ x ≤ b = 1/230,000 − 200000, 200,000 ≤ x ≤ 230,000 = 1/30000, 200,000 ≤ x ≤ 230,000 Everywhere else, the probability density function will just be 0. Therefore, the full probability density function for the sales price of a home follows. f(x) = _______________ 200,000 ≤ x ≤ 230,000 elsewhereIf Θ ∼ Uniform(a = 0, b = 3), find the probability density function of sin(Θ).Given the function y = x2 considered as a probability density distribution defined at 0 ⩽ x ⩽ 3, find the median and the first and third quartiles from the integral function
- Consider the following constant function: f(x) = 3/4 If this function represents a probability density function, which of the following can be a set of realized values? A. 2/3 ≤ x ≤ 2 B. 1/4 ≤ x ≤ 1 C. 3 ≤ x ≤ 4 D. 1/2 ≤ x ≤ 3/2Show that the following are probability density functions (pdf’s): b. f2(x) = 2e−2xI(0,∞)(x)Consider the function given below:f(x) = kx2 0 < x < 2.13What must be the value k so that f(x) is a valid probability density function?
- Suppose the unknown X satisfies −2 ≤ x ≤ 2 and has the probability density function fX (x)=C (4−x^2),−2 ≤ x ≤ 2 ,where C is a constant. What is the probability that |X| ≥ 1? Possible Answers: 10/16 21/32 5/16 3/32In a study of intelligence, the time (in seconds) for a laboratory animal to reach a reward in a maze was found to have a probability density function f(t) = 8 t 2 , t ≥ 8 where 8 seconds is the minimum time to traverse the maze. (a) Find the probability that an animal chosen at random takes between 28 and 56 seconds. (b) Find the probability that an animal chosen at random takes more than 28 seconds given that it took less than 56 seconds.From the density below the probability that X is at least 0.34 is what?