n to Probability (IE 231 01 02)E Introduction to Probability ( IE 231 01 02) / WEEK 12 / Homework 3Let Y be a random variable giving the number of heads minus the number of tails in three tosses of a coin. The coin is biasedas a tail. Considering the elements of the sample space S for the three tosses of the coin, find the cumulative distribution function value of F(1).that a head is twice as likely to occurAnswer.Next pageJump to.Next Activity

GivenRandom variable YY=(number of heads - number of tails) in three tosses of coin. The coin is…

Answered: Let Y be a random variable giving the…

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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Once all three lists are generated, add them to create the totals of the 200 trials. Create a discrete random variable relative frequency histogram for this data. Clearly label the axes and scale. Calculate the mean and standard deviation for the roll totals: μ= σ= Use these to define a normal probability distribution for the total on the roll of 3 dice. Compare the probabilities of the experimental discrete probability distribution and the normal curve distribution for several cases listed on the table. Complete the table. Probability Relative Frequency Histogram Normal Curve P(9.5≤x≤10.5) P(x≤3) P(x≥15) P(8≤x≤10) Write a brief paragraph comparing the results of the table above. Discuss any similarities or differences in these results. There are 216 possible outcomes for the roll of three dice. The theoretical probabilities for the outcomes of the roll of three six-sided dice are: Roll Probability 3…
Customers of a restaurant have been complaining about food poisoning over the past week. A health professional was called to investigate. She tested a representative sample of the eggs and reported that 24% of the sample eggs tested positive for the salmonella bacterium. If a second health professional tests 66 eggs at random, what is the probability that exactly 14 test positive for salmonella? Use a normal distribution to approximate the answer and write it as a decimal rounded to the nearest hundredth.
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The mean height of 15-year-old boys (in em) is 175 and the variance is 64. For girls, the mean is 165 and the variance is 64. Assuming that the two populations are nomally distributed. If eight boys and eight girls were sampled, then the probability that the mean height of the sample of boys would be higher than the mean height of the sample of girls 18: O 0 9878 O 0.0062 O 0.9938 0 9972 Let E[X(Y-1)] 10, E[X(Y#1)] 20, V(X) Then E(Y) 8. V(Y) 12 and V(X+Y) 30. O 14/5 12/5 2
Oxygen demand is a term biologists use to describe the oxygen needed by fish and other aquatic organisms for survival. The Environmental Protection Agency conducted a study of a wetland area. In this wetland environment, the mean oxygen demand was μ = 9.9 mg/L with 95% of the data ranging from 6.3 mg/L to 13.5 mg/L. Let x be a random variable that represents oxygen demand in this wetland environment. Assume x has a probability distribution that is approximately normal. (a) Use the 95% data range to estimate the standard deviation for oxygen demand. (b) An oxygen demand below 8 indicates that some organisms in the wetland environment may be dying. What is the probability that the oxygen demand will fall below 8 mg/L? (Round your answer to four decimal places.) (c) A high oxygen demand can also indicate trouble. An oxygen demand above 12 may indicate an overabundance of organisms that endanger some types of plant life. What is the probability that the oxygen demand will exceed 12…
Soledad and Tania are both high school students. The number of texts Soledad sends daily, S, is approximately Normally distributed with a mean of 100 and a standard deviation of 6 texts. The number of texts Tania sends daily, T, is approximately Normally distributed with a mean of 108 and a standard deviation of 8.1 texts. Assume that S and T are independent random variables. Let D = S – T. What is the probability that Soledad sends more texts on a randomly selected day? 0.104 0.214 0.786 0.896
We throw a fair dice. Let X denote the square of the difference between the smallest even number on the dice and the number appears on the dice. Determine the range and the probability distribution of X, draw the graph of the cumulative distribution function F of the random variable X and find the expected value and the variance of X.

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