Find a constant C such that p is a probability density function on the given interval and compute the probability indicated. Ce-x 1 + e-2x p(x) = (For a constant C, express numbers in exact form. Use symbolic notation and fractions where needed. For a probability, use decimal notation. Give your answer to four decimal places.) C = on (-∞0, ∞0) P(X ≤ 6) ≈

Q: 2 For the probability density function f 0) - 2ex20 - Ox<0 What is the distribution function f(2) d.…

A: cdfF(X)=∫x=0xf(x)dx

Q: Find the mean value of f(x) = |x| on the interval [-1, 4]. %3D

A: Given that: f(x)=|x| in [-1, 4]

Q: The graph attached is the uniform probability density function for a friend who is x minutes late.…

A: X~U(0,30) a=0  , b=30 X~U(a , b)

Q: For the probability density function, over the given interval, find E(x), E(x²), the mean, the…

A: Pdf of X is f(x)=∫0301450xdx, [0,30]

Q: Consider the following exponential probability density function: f(x) = for æ > 0 a. Write the…

A: a) The required formula is calculated as follows: Px≤x0=∫0x013e-x3dx=13e-x3-130x0=-e-x30x0=1-e-x03

Q: For the probability density function shown, what is the value ofh? f(x) ↑ 0.45 0.8 1.25 2.5 Cannot…

A: The total area under the probability distribution function is always equal to 1. Total area=1 Apply…

Q: 9. Let p(x) = 4 T(1 + (2x)²) for 20 (and p(a) = 0 if a <0). (a) Show that p is a probability density…

A: 9. Given that p(x)=4π1+2x2 for x≥0.  First, we have to show that p is a probability density…

Q: P(1.15 < Z < 2.77) =

A: X~N( 0 , 1 )   μ=0 , ?=1 (for standard normal distribution)   Z-score =( x - μ )/?

Q: Find k such that the function is a probability density function over the given interval. Then write…

A:

Q: 3. A function g(x) is a probability density function function g(x) = -&- 5z 5e is a probability…

A:

Q: Find Prob(3 < x < 7) given that the probability density function is f(x) = .2e:2ª,

A:

Q: Consider the following exponential probability density function. a. Which of the following is the…

A: X has exponential distribution and probability density function of X isf(x)=12e-x2   for x≥0

Q: Help: Suppose X ∼ Geom(p). Use the definition of the expectation to find E[X].

A: X~Geom(p)

Q: Which of the following tables shows a valid probability density function? Select all correct…

A: Conditions for the discrete probability distribution The sum of all probability is equal to 1. Each…

Q: Find the value of the constant a for which the following function g is continuous on (-∞0, 00).…

A: GIVEN: g(x) = aif x &lt; 3x2 - axif x ≥3