The point spread in sports betting is essentially a handicap towards the underdog, for example the point spread of the game this weekend between Cincinnati Bengals and Kansas City Chief in Cincinnati +3 or Kansas city is -3. If you place a bet on the bengals, Kansas city must win by less than 3 points for your bet to wim. If Kansas city wins by exactly 3 points then the bet is a push and your stake is returned. Now suppose you placed a bet of 100 dollars on the bengals on a website where they charge 10% commission (if you win $90) when line was CIncinati +3 or Kansas City -3 According to previous studies the final margin of victory for NFL team in a given game can be approximated as a normal variable with a mean of points spread line and a standard deviation of 12, however suppose the bengals just announced that their star receiver Chase would return this weekend which adds two points in favour of the bengals. In other words, we suppose that the winning margin now for Kansas City this weekend follows N(1,144) What is the expectation of the money you will win (write the answers in pnorm).
The point spread in sports betting is essentially a handicap towards the underdog, for example the point spread of the game this weekend between Cincinnati Bengals and Kansas City Chief in Cincinnati +3 or Kansas city is -3. If you place a bet on the bengals, Kansas city must win by less than 3 points for your bet to wim. If Kansas city wins by exactly 3 points then the bet is a push and your stake is returned. Now suppose you placed a bet of 100 dollars on the bengals on a website where they charge 10% commission (if you win $90) when line was CIncinati +3 or Kansas City -3 According to previous studies the final margin of victory for NFL team in a given game can be approximated as a normal variable with a mean of points spread line and a standard deviation of 12, however suppose the bengals just announced that their star receiver Chase would return this weekend which adds two points in favour of the bengals. In other words, we suppose that the winning margin now for Kansas City this weekend follows N(1,144) What is the expectation of the money you will win (write the answers in pnorm).
The point spread in sports betting is essentially a handicap towards the underdog, for example the point spread of the game this weekend between Cincinnati Bengals and Kansas City Chief in Cincinnati +3 or Kansas city is -3. If you place a bet on the bengals, Kansas city must win by less than 3 points for your bet to wim. If Kansas city wins by exactly 3 points then the bet is a push and your stake is returned. Now suppose you placed a bet of 100 dollars on the bengals on a website where they charge 10% commission (if you win $90) when line was CIncinati +3 or Kansas City -3 According to previous studies the final margin of victory for NFL team in a given game can be approximated as a normal variable with a mean of points spread line and a standard deviation of 12, however suppose the bengals just announced that their star receiver Chase would return this weekend which adds two points in favour of the bengals. In other words, we suppose that the winning margin now for Kansas City this weekend follows N(1,144) What is the expectation of the money you will win (write the answers in pnorm).
The point spread in sports betting is essentially a handicap towards the underdog, for example the point spread of the game this weekend between Cincinnati Bengals and Kansas City Chief in Cincinnati +3 or Kansas city is -3. If you place a bet on the bengals, Kansas city must win by less than 3 points for your bet to wim. If Kansas city wins by exactly 3 points then the bet is a push and your stake is returned. Now suppose you placed a bet of 100 dollars on the bengals on a website where they charge 10% commission (if you win $90) when line was CIncinati +3 or Kansas City -3 According to previous studies the final margin of victory for NFL team in a given game can be approximated as a normal variable with a mean of points spread line and a standard deviation of 12, however suppose the bengals just announced that their star receiver Chase would return this weekend which adds two points in favour of the bengals. In other words, we suppose that the winning margin now for Kansas City this weekend follows N(1,144) What is the expectation of the money you will win (write the answers in pnorm).
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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