1. Suppose the random variable X represents the failure or not of Edward's speaker woofer while...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
1. Suppose the random variable X represents the failure or not of Edward's speaker woofer while listening to reggae on Friday. Assume there is probability 0.8 that Edward blows up his woofer (woofer fails) while listening to reggae. a. What type of distribution should be used to describe this random experiment? b. What is the probability of the event, Edward does not blow up his woofer? c. Draw the appropriate density function for this distribution and mark appropriately the area under the density function representing probability of the event, Edward does not blow up his woofer. 2. Suppose the random variable X describes a fair 20 sided die. a. What type of distribution should the random variable X follow, so as to describe outcomes of rolls of this die? b. Since distributions generate data, write down 5 possible values that this distribution is likely to generate? c. What is the expectation of X, E[X]? d. What is the variance of X, V[X]? e. Let A = {even outcome}. Use the density function to find the probability of A, P[A]. f. Draw a plot of the density function for this distribution. Mark on the plot the area under the density function representing P[A]. 3. Suppose X ~ Uniform(1, 6) and Y ~ Uniform(1, 20). a. Which random variable has a larger variance, X or Y? b. Explain why your answer to a. makes sense intuitively. Use sentences and/or made up data. 4. Suppose an email message fails to send for 1 out of every 10000 emails you send. a. What's the probability that 1 out of the next 500 emails of yours fails to send? b. What's the probability that at most 1 out of the next 500 emails of yours fails to send? c. What's the probability that at least 2 out of the next 500 emails of yours fail to send? 5. Suppose that over the course of 365 days, 1 million radioactive atoms of Cesium-137 decayed to 977,287 radioactive atoms, giving a decay rate of \(\lambda = (1000000-977287)/365 = 62.23). Use the Poisson distribution to estimate the probability that on a given day, 50 radioactive atoms decayed. 6. Let X ~ Binomial (3, p). For what value of p is f(2|3, p) maximized? 1. Suppose the random variable X represents the failure or not of Edward's speaker woofer while listening to reggae on Friday. Assume there is probability 0.8 that Edward blows up his woofer (woofer fails) while listening to reggae. a. What type of distribution should be used to describe this random experiment? b. What is the probability of the event, Edward does not blow up his woofer? c. Draw the appropriate density function for this distribution and mark appropriately the area under the density function representing probability of the event, Edward does not blow up his woofer. 2. Suppose the random variable X describes a fair 20 sided die. a. What type of distribution should the random variable X follow, so as to describe outcomes of rolls of this die? b. Since distributions generate data, write down 5 possible values that this distribution is likely to generate? c. What is the expectation of X, E[X]? d. What is the variance of X, V[X]? e. Let A = {even outcome}. Use the density function to find the probability of A, P[A]. f. Draw a plot of the density function for this distribution. Mark on the plot the area under the density function representing P[A]. 3. Suppose X ~ Uniform(1, 6) and Y ~ Uniform(1, 20). a. Which random variable has a larger variance, X or Y? b. Explain why your answer to a. makes sense intuitively. Use sentences and/or made up data. 4. Suppose an email message fails to send for 1 out of every 10000 emails you send. a. What's the probability that 1 out of the next 500 emails of yours fails to send? b. What's the probability that at most 1 out of the next 500 emails of yours fails to send? c. What's the probability that at least 2 out of the next 500 emails of yours fail to send? 5. Suppose that over the course of 365 days, 1 million radioactive atoms of Cesium-137 decayed to 977,287 radioactive atoms, giving a decay rate of \(\lambda = (1000000-977287)/365 = 62.23). Use the Poisson distribution to estimate the probability that on a given day, 50 radioactive atoms decayed. 6. Let X ~ Binomial (3, p). For what value of p is f(2|3, p) maximized?
Expert Answer:
Posted Date:
Students also viewed these mathematics questions
-
MUST BE CORRECT ANSWERS A small software company has the following simplified cashflow, funded by shareholders' equity of 20,000 and a bank overdraft of 5000: Invoiced money received 2 months after...
-
Construct, with explanation, the SLR(1) action and goto matrices for the above grammar. [5 marks] Illustrate how the SLR(1) parsing algorithm works for this grammar by showing the successive states...
-
Dun and Bradstreet have reported that nearly half of all Australian businesses operated with a negative cash flow over recent financial years. This figure is worrying as 80% of business failures are...
-
In the following figure, a consumer is initially in equilibrium at point C. The consumers income is $ 400, and the budget line through point C is given by $ 400 $ 100X + $ 200Y. When the consumer is...
-
Sparkle Floral offers a special-priced arrangement for holidays and business increases significantly during these specials. Bella, the owner of Sparkle, guarantees customer satisfaction and charges...
-
Nancy operates a business that uses the accrual method of accounting. In December, Nancy asked her brother, Hank, to provide her business with consulting advice. Hank billed Nancy for $7,800 of...
-
What is the difference between a strepsirhine and a haplorhine?
-
How can forensic anthropologists contribute to making an identification, and how is DNA evidence used in forensic anthropology? What is the difference between perimortem and postmortem trauma?
-
In each of the following, name the term defined or answer the question. Answers are listed at the bottom. 1. Three terms commonly used to refer to a layout where similar equipment or functions are...
-
What determinations are included in an individuals biological profile?
-
How do we define a primate?
Study smarter with the SolutionInn App