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In Exercises 1–8, use Bayes’ theorem or a tree diagram to calculate the indicated probability. Round all answers to four decimal places. [HinT: See Quick Example 1 and Example 3.]
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- What value(s) of w will make this discrete probability model illegitimate? A. w > 0.1 B. w = 0.1 C. w < 0.1 D. Both A & C.arrow_forward4.3#2. An article suggests that substrate concentration (mg/cm3) of influent to a reactor is normally distributed with ? = 0.70 and ? = 0.08 What is the probability that the concentration exceeds 0.90? What is the probability that the concentration is at most 0.60? The largest 5% of all concentration values are above?arrow_forwardA system consists of four components connected as shown below in the following diagram.Assume ?, ?, ?, and ? function independently. If the probability that ?,?, ?, and ? fail are 0.10, 0.05, 0.10, and 0.20 respectively. What is the probability that the system functions?b) A process manufactures ball bearing whose diameters are normally distributed with mean 2.505?? and standard deviation 0.008??. Specifications call for the diameter to be in the interval 2.5 ± 0.01 cm. what proportion of the ball bearings will meet the specificationarrow_forward
- Let X be a Poisson random variable with E(X) = 3. Find P(2 < x < 4).arrow_forwardSuppose a world has two risky assets: HotPot and IceCream. The following table shows the holding period returns in each scenario. Suppose the T-bill rate is 5%. Scenario Probability Return (HotPot) Return (IceCream) Rainy 0.02 10% -5% Snowy 0.03 15% -15% Windy 0.9 10% 8% Sunny 0.05 -10% 25% Which answer is the closest value to the fifth-percentile value at risk (VaR) of holding IceCream? A. -15% B. -5% C. 25% D. -10%arrow_forwardyour task is to calculate the P(E) using Kolmogorov's Axioms for probability functions.arrow_forward
- a) Let X be a random variable and let E[X] =marrow_forwardAn investment firm offers its clients municipal bonds that mature after several years. Since the cumulative distribution function of T the number of years to maturity of a randomly chosen bond, is img Calculate the following probabilities P(T>3)= ? P(1.4<T<6)=?arrow_forwardThe diameter of a round rock in a bucket, can be messured in mm and considered a random variable X in f(x) f(x) = k(x-x4) if 0 ≤ x ≤ 1f(x) = 0 otherwise. Find the expectation E(4X+ 3) and variance V(4X+3)arrow_forward
- (a) The monthly returns on two securities A and B are both known to be normally distributed, with the following parameters: Security Expected monthly Return, E(Ri) Standard Deviations of monthly Return, SD(Ri)A 3% 4%B 2% 3% Correlation between monthly returns: corr(RA, RB) = rAB = 0.3 An investor intends to create an equally-weighted portfolio by investing equal amounts in securities A and B at the start of each month. (i) What is the probability that the monthly return on security A is negative? (ii) What are the expected monthly return and the standard deviation of the monthly return on the equally-weighted portfolio? (iii) What is the probability that the monthly return on the equally-weighted portfolio is negative? (b) Six prize…arrow_forwardMendel found no dominance in snapdragons, with one red gene and one white gene producing pink-flowered off-spring. These second-generation pinks, however, still carry one red and one white gene, and when they are crossed, the nextgeneration still yields the Punnett square from Exercise 87.Find each probability.a. P(red)b. P(pink)c. P(white)(Mendel verified these probability ratios experimentallyand did the same for many characteristics other than flowercolor. His work, published in 1866, was not recognizeduntil 1890.)arrow_forwardRefer to Exercise 15. Let E1 be the event that the wafer comes from Lot A, and let E2 be the event that the wafer is conforming. Are E1 and E2 independent? Explain.arrow_forward
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