A random variable X follows the continuous uniform distribution with a lower bound of −2 and an upper bound of 16. a. What is the height of the density function f(x)? (Round your answer to 4 decimal places.) b. What are the mean and the standard deviation for the distribution? (Round your answers to 2 decimal places.) c. Calculate P(X ≤ 1). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)

a. Height=0.0555

b. Mean=7

SD=4.0415

c. P(x≤1)=0.1665

Step-by-step explanation:

a. If we have a continous uniform distribution, we have a density function that is a constant:

In the other hand, the cumulative density function across the entire region should be one:

Then the height C of the density function is 0.0555.

b. The mean of this distribution is:

The standard deviation of this distribution is:

c.

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.