Eagles always lay three eggs at a time. The number of eggs that hatch is described by the following probability distribution. x = 0, 1, 2, 3 P(X = x) = 0.1, 0.3, 0.4, 0.2 Create a histogram of the data and find the expected value or mean.

An automotive center keeps track of customer complaints received each week.  The probability distributions of complaints are shown below.  The random variable, xi, represents the number of complaints, and p(xi) is the probability of receiving xi complaints for two of the stores. The cost impact of each complaint is believed to be y=$10x3 where x is the number of complaints. Store A xi 0 1 2 3 4 5 6 p(xi) 0.10 0.15 0.20 0.25 0.15 0.10 0.05     Store B             xi 0 1 2 3 4 5 6 p(xi) 0.10 0.15 0.25 0.22 0.13 0.08 0.07 The Manager provides the following utility function to evaluate the two stores. xi 0 1 2 3 4 5 6 u(xi) 1.00 0.60 0.40 0.20 0.10 0.05 0.00 Which store does the Manager prefer as having fewer complaints? Compare using utility as the metric with using the average number of complaints as the criterion for deciding which Store is better (or…

Use the probability distribution to complete parts (a) and (b) below. The number of defects per 1000 machine parts inspected Defects 1 2 4 Probability 0.264 0.290 0.240 0.148 0.042 0.016 ..... (a) Find the mean, variance, and standard deviation of the probability distribution.

On average, you receive 2.6 pieces of junk mail a day. Assume that the number of pieces of junk mail you receive each day follows the Poisson distribution. What is the probability that you receive exactly three pieces of junk mail today? A 0.2196 B 0.2167 C 0.1276 D 0.2176

An automotive center keeps track of customer complaints received each week.  The probability distributions of complaints are shown below.  The random variable, xi, represents the number of complaints, and p(xi) is the probability of receiving xi complaints for two of the stores. The cost impact of each complaint is believed to be y=$10x3 where x is the number of complaints. Store A xi 0 1 2 3 4 5 6 p(xi) 0.10 0.15 0.20 0.25 0.15 0.10 0.05     Store B             xi 0 1 2 3 4 5 6 p(xi) 0.10 0.15 0.25 0.22 0.13 0.08 0.07   Sample from these distributions to compute the total number of complaints (store A+B) per week for 52 weeks.

Neighborhood Insurance sells fire insurance policies to local homeowners. The premium is $150, the probability of a fire is 0.1%, and in the event of a fire, the insured damages (the payout on the policy) will be $140,000. g. What are the expected value and variance of your profit?

When practicing basketball, Rachel has a 67% chance of making a free throw. She shoots 12 free throws. Let the random variable X be the number of free throws she makes. Find the probability she makes exactly 5 free throws. Give your answer to at least three nonzero decimal places. What is the expected value of X. Interpret this value.

4.43 Consider the probability distribution for the random vari- able x shown here: 2 .4 10 .2 1 4 P(x) 2

Use the probability distribution to complete parts​ (a) and​ (b) below.     The number of defects per 1000 machine parts inspected Defects 0 1 2 3 4 5   Probability 0.255 0.294 0.235 0.158 0.042 0.016       ​(a) Find the​ mean, variance, and standard deviation of the probability distribution.   The mean is enter your response here. ​(Round to one decimal place as​ needed.)

Verify whether the given table represents a probability distribution.  In those cases where a probability distribution is described, find the mean and standard deviation. NOTE: The Rounding Rule for the mean and standard deviation: They should be rounded to one more decimal place than occurs in the raw data. For a group of four students, the number y who takes the Calculus II class next semester is given by this table. y           P(y) 0           0.5131 1            0.3139 2           0.0624 3           0.1102 4           0.2002 Probability distribution with μ=0.4 and σ=0.4 Probability distribution with μ=0.6 and σ=0.1 Probability distribution with μ=0.6 and σ=0.3 Probability distribution with μ=0.7 and σ=0.4