Question

2. For each of the following random variables:

• Decide whether it would be appropriate to model it as a Bernoulli, binomial, geometric, or Poisson distribution, or none of the above. Explain briefly why these choices are appropriate, including any independence assumptions. If appropriate, give the parameter value(s).

• Determine the expected value, variance, and standard deviation of the random variable. If it follows one of the special distributions, you can use the known formulas discussed in class. (If multiple choices would be appropriate, then give the expectation / variance / standard deviation values for all the choices, if they are different.)

If it doesn’t follow a special distribution, then compute these values yourself in some appropriate way.

(a) In Rocky Mountain National Park, there is a probability 0.0001 for any given hiker to see a bear. On Sunday, 8000 people went hiking in the park. Let X be the total number of hikers who saw a bear.

(b) Whenever Nate goes for a hike, there is a 13% chance that he will lose his hat. Let Y be the number of hikes that Nate can take before he has to buy a new hat.

(c) 15 people go for a hike. Each of them has probability 0.86 of being bit by a mosquito. Let W be the number of people who are bit.

(d) Fred is hiking a loop trail that is 2.8 miles long. It is so much fun that each time he finishes, there is a 40% chance that he will decide to keep going and hike it again. Let M be the total number of miles that Fred hikes.

Answer 1

Tİtal number et hikes -800。 the beak x- total umber of hikes whe Sau Sne hikes ethe beal nden beat th 6 she → x ~ Bivernial (goo o, o.ooo.) 00 xO 0o0l xo.9999-0.79992 Stundad Pabability He psobability of Joreing 0.894 3 a niau hat i he Jocs this hat the hat in na hikes hat in 6n-1) hikeg uioxpuebability of leting hat in nth hike hence y is a Cneemetie Randon Vasiable

e13 1.642 Extuctation et of y =7-692 Standard daviadien et all 15 5. 47 sut te henta 151 0.86 ん~ Binar ial (15,0,86) Entactatien (W) = 15x0.86 = 12.9 Standasd dewichion- Vaiankst()1.3438 hike 0.4 Tetal number Mileg ied hikes M2.8y .6667 miles -0.6 aliance ( M ) o 62 Sod (Vatiand 1l) 2.5 mile S tandal dald M)-) Valiante (M) ぢ 2.95