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Distrubution of sum of two random variables
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- Safety switch An industrial machine requires an emer-gency shutoff switch that must be designed so that it can be easily operated with either hand. Design an experi-ment to find out whether workers will be able to deacti-vate the machine as quickly with their left hands as with their right hands. Be sure to explain the role of random-ization in your design.Example Compute the expected value of a Bernoulli random variable.Distinguish between discrete random variable and continuous random variable. Why time cannot be measured in a discrete scale?
- 6- The variance of the sum of the random variables equals the sum of the variances if the random variables are uncorrelated. True O FalseGrace Floral Shop sells several types of roses for all occasions. It is known that 43% of the roses that is sold by Grace Floral Shop are Eden Roses. 12 roses are ordered to put in a bouquet(i) Define the random variable for this situation and list its values (ii) Stating its parameter(s), what is the probability distribution of this variable? (iii) State the conditions that influence your choice of distribution.Suppose on a fair 8-sided die, The gambler rolls the die where the gambler loses $6 if a 1,2,3, or 4 is rolled. While on a roll of 5, 6, 7, 8 the gambler wins that amount. Let Q be the random variable representing the gambler's wins/losses in dollars. What is the variance of Q? "Show the process" Pick the correct Answer. - 3/8 9/2 371/64 35/4 75/2 635/16
- Modeling and Simulation (Geometric Distribution) Q1) At Colombia University, each student has a probability of 0.8 to pass the simulation exam. Denote by X the random variable that represents the number of times a student must take the simulation exam in order to pass it (assume independent outcomes for each trial, and that probability of success remains the same). a) What is the average number of times a student has to take the exam?Modeling and Simulation (Geometric Distribution) Q1) At Colombia University, each student has a probability of 0.8 to pass the simulation exam. Denote by X the random variable that represents the number of times a student must take the simulation exam in order to pass it (assume independent outcomes for each trial, and that probability of success remains the same). a) What is the average number of times a student has to take the exam?Game of chance: A player rolls a fair six-sided die. If outcome of a roll is an odd number, the player wins as many dollars as there are dots on the top face . Otherwise, the player looses 4 dollars. Let the random variable X be profit (amount won or lost) per game. Make a probability distribution table for the random variable: amount won or lost. Find the Expected value of the experiment Use Law of Large numbers to interpret the meaning of the Expected value If a person plays 100 times, how much he expects to win/loose?
