f(x)=3x² 2 0 ≤ x ≤ 1 a) Verify that (x) is a probability density function b) Find the CDF F(x) c) Find Pr (0.25 ≤ X ≤ 0.75) AQAAAAAAAAAAAAAAAAAAAAA
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- The probability density function of the continuous random variable X is given by: img Calculate: E(X)= ? V(X)= ? P(0.8<X<1.2)= ? Note: Answer with at least 4 decimal placesLet f(x) = k(3x - x²) if 0 ≤ x ≤ 3 and f(x) = 0 if x 3. a) For what value of k is f a probability density function? b) For that value of k, find P(X > 1).Let the cumulative distribution function of a distribution is given by: I 3.5. Determine the probability density function f(r) of the distribution.
- If X has the probability density * 21 f(2): 2 <1 Find P (1 < X < 5). Select one: O a. 0.93 O b. 0.96 O G 0.12 O d. 0.91: say in each case, if the function f is a probability density over interval I. a) f (x) = 0.5x + 0.5 on I = [-1; 1] b) f (x) = x on I = [0; 1] c) f (x) = 0.5 on I = [-1; 1] d) f (x) = -2x² + 2 over I [0; 1]part C D
- The probability density function of a random variable X is fX(x) { b(1 −x)4 0 ≤x ≤1 , 0 elsewhere (a) Find b such that fX(x) is a valid density function. (b) Find the probability that X is less than 1/2. (c) Find the probability that X is less than 1/4 given that X < 1/2|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(0.25Solve using R. Show all work.A random variable X has a probability density function equal toWhere p is a constant in the interval [0, 1] and C is another constant. Ask:a) Find C so that fX (x) is a probability density function valid.b) Determine the generator function of moments MX(s) of V.A. X.c) Use MX(s) to calculate E{X}.d) Use MX(s) to calculate E {X2}e) Determine the variance of X.Consider the probability distribution function (PDF) f(r) = Ax sin r, for 0|f(x)dx = 1 Find the 2 Let x be a continuous random variable over [a,b] with probability density function f. Then the median of the x-values is that number m such that a median. 1 f(x) = 50 x, [0,10] ... The median is m=Recommended textbooks for youCalculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage Learning
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