(a) (b) (c) f (x) = c exp (- 6x) x > 0 - cx, -1 < x≤0 0, otherwise f(x)= cx² exp(-x²) x > 0 S(x)=√(²3)*, x = 0,1,2,...
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- Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.Let the probability function of the random variable X bef(x) = { x/45 if x = 1, 2, 3, ⋯ ⋯ ,9 { 0 otherwiseFind E(X) and Var(X)Let Y be a continuous random variable with cumulative distribution function: A A B B C C D D E E F(y) = 1-e-(y-a)², where a is a constant. What is the 75th percentile of Y? (A) F(0.75) (B) -√2 In ¹ √2 In ¹ (C) (D) a - 2 Vln2 (E) a +2√In2 a- a + for y ≤ a otherwise
- X is a continuous random variable having p.d.f. f(x) such that f(x) = kr Osx55 otherwise Find : (a) the constant k; (b) P(15XS 2); (c) (d (e) (f) E(X); E(3X + 1); E(X?); Var (X); (g) Var (4X - 5);3 probabilty densit function of a random variable is an even function. Note: is an even function if probability dense functionsfx (x) of a random variable X is an even function , meaning fx (x) = fx (-x) . Let Y = - x .show that X and Y are identically distributed Why is the solution 1- FunctionX(-y) = FunctionX(y)? why are those two equal? Can you please explain how to have the answer step by step? please explain not just solveThe probability distribution for a random variable X is given by Pr(X = x) = (3x + 1)/22, x = 0, 1, 2, 3. Determine (a) Pr(X = 3); (b) Pr(X <= 1); (c) Pr(1 <= X < 3); (d) Pr(X > -2); and (e) Pr (X = 1|X <= 2).
- (b) Find the variance Var(X) of X.The lung cancer hazard rate λ(t) of a t-year-old male smoker is such that λ(t) = 0.027 + 0.00025(t-40)2, and t >= 40. Assuming that a 40-year-old male smoker survives all other hazards, (a) what is the probability that he survives to age 50 without contracting lung cancer?(b) what is the probability that he survives to age 60 without contracting lung cancer?The variance for the binomial probability distribution is var(x) = P(1 - P) var(x) = nP var(x) = n(1 - P) var(x) = nP(1 - P)
- A random variable X takes values 0,1,2 where E(x) =1.5, var(x)=0.25 then E (3x– x² +4) =If F(x) is cumulative distrbution function of a continuous random variable X, the probability (function f(x) is the dervative of F(x (Fa)se (TrụeLet f(x, y) = x + y for 0 < x < 1 and 0 < y < 1 The Conditional Variance of Y when X = ; is