3. The (g) what is the standard deviation of # of accidents per day? random vari

ID: 3064199 • Letter: 3

Question

3. The (g) what is the standard deviation of # of accidents per day? random variables defined in Examples 1 to 3 are indeed Binomial random variables. Check and identify each of the conditions for a valid binomial random variable using the following table. Example 4 followed after the table is a discrete random variable. You are asked to determine if the random variable follows a binomial distribution. Exmaplel: A sample of four parts is randomly chosen from a manufacturing process. From the previous observation, the defective rate is .2-Let X is the # of defective parts in the sample. Example 2: Tossing a fair coin 100 times. Let X be # of heads occur Example 3: A survey of asking 20 randomly chosen individuals their preference of voting based on either credential or party. Suppose that the previous history showed the probability of prefem X be the # of individuals preferring·Party, in the sample Properties to be checked ion four s at random Tossing a fair coin 100 times ey 20 voters Is each trail approximately identical? How many? or each trail, what is 'Success', "Failure? For each trial, what is P(S), P(F)? Think about how a trial is conducted. Are they independent from trail to trail? Think about the random variable X. What are the possible values for X? Is X as defined a Binomial Random Variable Yes/No) If X is a Binomial random variable, what is the shape of the distribution? If the distribution is a Binomial distribution, find ECX) and s.d.x) Example 4: X is the number of falls during the ice skating competing performance per athlete in the Winter Olympics game. Is the random variable X a Binomial random variable? Why?

Explanation / Answer

Is each trial approximately identical? how many?

YES

FOUR

YES

100

YES

For each trial what is "success", "failure"

success: A defective part is found.

failure: A non-defective part is found

success: Head occurred

failure: tail occurred

success: person preferring party observed

failure: a person not preferring the party observed

P(S)=0.2

P(F)=0.8

P(S)=0.5

P(F)=0.5

P(S)=0.7

P(F)=0.3

E(X)=4(0.2)=0.8

s.d(X)=0.8

E(X)=50

s.d(X)=5

E(X)=14

s.d(X)=2.05

example 4: the random variable here is not binomial as the probability of falling is not same in each trial.

Hope this is helpful.THANK YOU

Properties to be checked Inspection four parts at random Tossing a fair coin 100 times survey 20 voters