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Expected Value01:15

Expected Value

The expected value is known as the "long-term" average or mean. This means that over the long term of experimenting over and over, you would expect this average. The expected average is represented by the symbol μ. It is calculated as follows:
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Determination of Expected Frequency01:08

Determination of Expected Frequency

Suppose one wants to test independence between the two variables of a contingency table. The values in the table constitute the observed frequencies of the dataset. But how does one determine the expected frequency of the dataset? One of the important assumptions is that the two variables are independent, which means the variables do not influence each other. For independent variables, the statistical probability of any event involving both variables is calculated by multiplying the individual...
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Flat Belts: Problem Solving01:28

Flat Belts: Problem Solving

Flat belts are crucial in many industrial applications as they help transmit power from one pulley to another. The concept of forces and moments is used to determine the maximum moment on a pulley. For instance, consider a flat belt that wraps around two pulleys, A and B, with radii of 30 cm and 10 cm, respectively. The angle between the belt and the horizontal is 20 degrees at the pulleys. As pulley B rotates clockwise and drives pulley A, tension T2 is caused at one end of the belt, while...
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Frictional Forces on Flat Belts01:28

Frictional Forces on Flat Belts

Flat belts are commonly used in various industrial applications for transmitting power from one pulley to another. When a flat belt is wrapped around a set of pulleys, it experiences different tensions at the driving pulley ends due to the friction between the belt and pulley surface. When the pulley moves in a counterclockwise direction, the tension T2 on the opposite side of the pulley where the belt is moving away from is higher than the tension T1 on the side where the belt is moving...
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Expected Frequencies in Goodness-of-Fit Tests01:19

Expected Frequencies in Goodness-of-Fit Tests

A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n)  to the number of categories (k).
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Fluid Pressure over Flat Plate of Constant Width01:05

Fluid Pressure over Flat Plate of Constant Width

When a body is submerged in water, it experiences fluid pressure acting normal on its surface and distributed over its area. For better design structures, it is crucial to determine the magnitude and location of the resultant force acting on the surface. In the case of a rectangular plate of constant width submerged in water, the pressure increases with depth, resulting in a linearly varying trapezoidal pressure distribution from the upper to the lower edge of the plate.
The resultant force...
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