Consider the discrete probability distribution for the variable X below. Value of XProbability of that value00.310.520.130.1 (a) Verify that this is a discrete probability distribution. Be sure to show both conditions.(b) Compute the probability of getting a value of two.(c) Compute the probability of getting a value at least 1.(d) Compute the mean value of X. Do not use statistical features of your calculator.(e) Compute the standard deviation value of X. Do not use statistical features of your calculator.

Given data is Value of X Probability of that value 0 0.3 1 0.5 2 0.1 3 0.1

Answered: Consider the discrete probability…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 13E

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Consider the discrete probability distribution for the variable X below.

Value of X	Probability of that value
0	0.3
1	0.5
2	0.1
3	0.1

(a) Verify that this is a discrete probability distribution. Be sure to show both conditions.

(b) Compute the probability of getting a value of two.

(d) Compute the mean value of X. Do not use statistical features of your calculator.

(e) Compute the standard deviation value of X. Do not use statistical features of your calculator.

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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