A police department reports that the probabilities that 0,1,2, and 3 burglaries will be reported in a given day are .51, .44, .04, and .01, respectively. Find the expected number of burglaries reported in a given day.

How do I figure this out? I simply do not know. Help, please?

In 100 days, how many burglaries?

44(1) + 4(2) + 1(3) = 55
55/100 =

To find the expected number of burglaries reported in a given day, you need to multiply each possible outcome (0, 1, 2, 3 burglaries reported) by their respective probabilities, and then sum up these products.

Let's calculate it step by step:

1. Multiply the probability of each outcome by the number of burglaries reported for that outcome:
- Probability of 0 burglaries (0 x 0.51) = 0
- Probability of 1 burglary (1 x 0.44) = 0.44
- Probability of 2 burglaries (2 x 0.04) = 0.08
- Probability of 3 burglaries (3 x 0.01) = 0.03

2. Sum up the products:
0 + 0.44 + 0.08 + 0.03 = 0.55

The expected number of burglaries reported in a given day is 0.55.

So, based on the given probabilities, the police department expects approximately 0.55 burglaries to be reported in a given day.

To find the expected number of burglaries reported in a given day, you can use the formula for expectation:

E(X) = ∑ (x * P(x))

where E(X) is the expected value, x is the possible number of burglaries reported, and P(x) is the probability of x burglaries being reported.

In this case, we have the probabilities listed as:

P(0) = 0.51
P(1) = 0.44
P(2) = 0.04
P(3) = 0.01

To calculate the expected number of burglaries reported, we multiply each possible number of burglaries by its corresponding probability, and then sum up the results:

E(X) = (0 * 0.51) + (1 * 0.44) + (2 * 0.04) + (3 * 0.01)

E(X) = 0 + 0.44 + 0.08 + 0.03

E(X) = 0.55

Therefore, the expected number of burglaries reported in a given day is 0.55.