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How is the probability distribution of a random variable constructed?Usually, the past behavior of the variable is studied and the frequency distribution of the past data is formed. If the past behavior can be taken as a representative pattern of the future also, then the past frequency distribution can be used as a guide for predicting the future values of the random variable. If past behavior cannot help, then a subjective probability distribution of the likely future values is formed on the basis of expert opinion.
The issue pattern of a component AB323 as observed by the storekeeper of XYZ Limited over the past one hundred working days has been summarized below.
Number Issued
No. of days
100
1
101
2
102
3
103
5
104
6
105
7
106
9
107
10
108
12
109
11
110
111
8
112
113
114
4
115
From the above table, in addition to observing that the issues have ranged between 100 units to 115 units, the storekeeper can also assess the chances of each quantity being issued by forming a probability distribution.
The probability distribution can be formed by dividing the individual values by 100 (the total number of days over which the observations have been made).
Number issued
Probability that the Random Variable will take on this value
0.01
0.02
0.03
0.05
0.06
0.07
0.09
0.10
0.12
0.11
0.08
0.04
Total
1.00
The probability distribution of a random variable provides a probability for each possible value and the probabilities must sum to 1.
Q. Example of negative number? If you take an elevator 8 stories down , what would be the opposite of this? The opposite would be that you take the elevator 8 stories up .
Can you explain that a wave through the origin always has a slope of one or not?
Assume that Y 1 (t) and Y 2 (t) are two solutions to (1) and y 1 (t) and y 2 (t) are a fundamental set of solutions to the associated homogeneous differential equation (2) so, Y
Trapezoid Rule - Approximating Definite Integrals For this rule we will do similar set up as for the Midpoint Rule. We will break up the interval [a, b] into n subintervals of
5 2 ----- - ----- x-1 x+1 -------------------- x 1 ----- + ----- x-1 x+1
what is the differeance in between determinate and matrix .
Define A*B where: A = | 3 -3 6 | B = | 6 1 | | 0 4 2 | | 0 -5 |
Write a procedure to obtain the inverse of an n by n matrix usingGaussian elimination. (You cannot use A - 1 or any of the built-in packages like 'MatrixInverse'.) Output any a
(4 sqrt3+5 sqrt2)/(sqrt48+ srt18)
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