nment: Chapter 5 Assignmentstions Exercise 05.32 Algo (Binomial Probability Distribution)O Consider a binomial experiment with n = 8 and p = 0.1.a. Compute f(0) (to 4 decimals).f(0) =b. Compute f(3) (to 4 decimals).f(3)c. Compute P(x ≤ 1) (to 4 decimals).P(x ≤ 1) =d. Compute P(x 24) (to 4 decimals).P(x ≥ 4) =e. Compute E(x) (to 1 decimal).E(x)f. Compute Var (x) and o.Var(x) ===σ=Q Icon Key(to 2 decimals)(to 2 decimals)

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A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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7.2.1. X is the binomial (5, 1/2)random variable. Find PxB(x), where the condition B = {X 2 ux}. What are E[X\B]and Var[X\B]?
6. We have three light bulbs with lifetimes T1, T2, T3 distributed according to Exponential(A1), Exponential(A2), Exponential(A3). In other word, for example bulb #1 will break at a random time T1, where the dis- tribution of this time T1 is Exponential(A1). The three bulbs break independently of each other. The three light bulbs are arranged in series, one after the other, along a circuit- soon as one or more light bulbs fail, the circuit will break. Let T be the lifetime of the circuit-that is, the time until the circuit breaks. -this means that as 1 (a) What is the CDF of T, the lifetime of the circuit? (b) Next, suppose that we only check on the circuit once every second (assume the times T1,T2,T3,T are measured in seconds). Let S be the first time we check the circuit and see that it's broken. For example, if the circuit breaks after 3.55 seconds, we will only observe this when 4 seconds have passed, and so S = 4. Calculate the PMF of S. (c) Finally, suppose that instead of…
Consider a binomial experiment with n = 14 and p = 0.5. a. Compute f(0) (to 4 decimals). f(0) = b. Compute f(3) (to 4 decimals). f(3) = %3D c. Compute P(r 4) = e. Compute E(x) (to 1 decimal). E(r) = f. Compute Var(z) and o. Var(x) = (to 2 decimals) (to 2 decimals)
Consider a binomial experiment with n = 14 and p = 0.3. a. Compute f(0) (to 4 decimals). f(0) = b. Compute f(5) (to 4 decimals). f(5) = c. Compute P(x 2) (to 4 decimals). P(x > 2) = e. Compute E(x) (to 1 decimal). E(x) = f. Compute Var(x) and o. Var(x) = (to 2 decimals) O = (to 2 decimals)
Consider a binomial experiment with n = 10 and p =0.1. a. Compute f(0) (to 4 decimals). /(0)% = b. Compute f(5) (to 4 decimals). f(5) = c. Compute P(2 4) = e. Compute E(2) (to 1 decimal). E(x) = f. Compute Var(a) and a. Var(x)= (to 2 decimals) (to 2 decimals)
Event A is my wife cooking dinner tonight. It has been determined that P(A) = 0.15. What is P(not A)?
2. Find E(X) and Var(X) if a. P(X = 0) = 0.2, P(X = 1) = 0.3, and P(X = 2) = 0.5. b. X is the number of successes in 200 Bernoulli trials each with probability of success 0.7.

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