**Question 5:** Using the Poisson Formula, find the following Probabilities:1. $ P(x \leq 2); \, \lambda = 6 $2. $ P(x = 1); \, \lambda = 4 $3. $ P(x \leq 3); \, \lambda = 5 $(Note: There are no graphs or diagrams associated with this problem.)

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Answered: Question 5: Using the Poisson Formula,…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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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1. ABC inc. stock is currently selling for $30, one year from today the stock price can either increase by 20% or decrease by 15%. The probability of an increase in the stock price is equal to 0.3. The one-year risk-free rate is 5% What is the value of a European put that expires in one year with an exercise price of $24. 2. Graphically, show the value and the profit and loss of the following butterfly position: Long in a call with an exercise price of $30, short in 2 calls with an exercise price of $45, and long in a call with an exercise price of 60. All calls are written on the same stock and have the same maturity. 3. "Early exercise of an American option on a stock that does not pay any dividend is not optimal regardless of whether the option is a Call or a Put". True, False, or Uncertain. Explain.
Let X₁ and X₂ be independent r.v.'s having the same distribution, taking on values 0 and 1 with respective probabilities 0.2 and 0.8. Answer Questions 12 and 13 below. Question 12 Write the m.g.f. of X₁ + X₂ + 2. (0.2+0.8e²) ²% e²z ○ (0.2e + 0.8e²x) e²z (1 + 0.² e² )² e²² (0.2+0.8e²)² e²z Question 13 Write the m.g.f. of X₁ – 2X₂. (0.2 +0.8e²) (0.2 +0.8e-2²) (0.8e + 0.2e²) (0.2e + 0.8e-2²) (0.2e +0.8e²) (0.2e-² +0.8e-²²) O (0.2e² +0.8e-²) (0.2e + 0.8e²)
The probability of afternoon rain given morning cloud cover >50% is of interest to those forecasting the weather. You can calculate this probability using Bayes' Theorem (below). The probability of morning cloud cover in general is 30% in the area you are concerned with and when there's afternoon rain, morning cloud cover of the kind described above occurs 90% of the time. The probability of rain in general for the area is about 26% of days. From the above information, identify what P(BIA) would be. Express your answer as a proportion, rounded to two decimal places. P(A/B)= = P(B|A)*P(A) P(B)
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QUESTIÓN 6 Assume that a researcher randomly selects 14 newborn babies and counts the number of girls selected, x. The probabilities corresponding to the 14 possible values of x are summarized in the given table. Answer the question using the table. Probabilities of Girls x(girls) P(x) x(girls)| P(x) x(girls) P(x) 0.061 0.000 0.122 10 1 0.001 6 0.183 11 0.022 2 0.006 7 0.209 12 0.006 3 0.022 0.183 13 0.001 4 0.061 9 0.122 14 0.000 Find the probability of selecting exactly 5 girls. O 0.022 O 0.122 O 0.061 O 0.001
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Question 5: Using the Poisson Formula, find the following Probabilities: 1. P(xs2); A = 6 2. P(x=1); A = 4 3. P(xs3); A = 5