Probability, Random Variables, and Probability Distributions

Only even sums will occur

All values are less likely

It does not change from a single die roll

More values and more likely outcomes for middle sums

Multiply each observation by that constant before calculating variance.

Square root each observation multiplied by that constant before calculating variance.

Multiply the variance of the original variable by the square of that constant.

Add that constant to each observation before calculating variance.

.25

.50

.75

.00

P(A and B) = P(A) * P(B)

P(A or B) = P(A) + P(B)

P(A or B) = P(A) * P(B)

P(A or B) = P(A) + P(B) - P(A)*P(B)

Normal distribution with a mean of 15 and standard deviation of $\sqrt{20}$

Uniform distribution between the minimum possible value of X+Y and maximum possible value

Normal distribution with a mean of 8 and standard deviation of $\sqrt{20}$

Binomial distribution with parameters n = 8 and p = 5/8

Less than or equal to 20.

Between 60 and 70.

Greater than or equal to 90.

It appears easy to take sum of one or another but remember – we're talking about how varied results can be not their commonality or frequency.

The temptation might be thinking this situation requires taking average but actually since chances are not related we don't combine like that.

The product of deck shuffling variance and coin tossing variance since the events are independent and combined variance multiplies, they must be thought together.

Since cards and coins have different types of chances adding them up as if they were alike isn't correct approach we need to multiply.

Approximately 4.47

Approximately 3.61

Exactly 2

Exactly 5

30

15

200

Cannot be determined from the given information

95

70

60

32