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marta [7]
3 years ago
7

negative binomial rv is the number of failures that occur before the rth success in a sequence of independent and identical succ

ess/failure trials. The probability mass function (pmf) of X is
Mathematics
1 answer:
astra-53 [7]3 years ago
8 0

Answer:

The probability mass function (pmf) of X is:

P(X=k)={{k+r-1}\choose k}\cdot (1-p)^{k}\cdot p^{r};\ k=1,2,3,...

Step-by-step explanation:

The random variable <em>X</em> is said to be a Negative Binomial random variable.

The random variable <em>X</em> is defined as the number of failures in a series independent and identical Bernoulli trials, before a specific number of success takes place.

For example, consider rolling a 5 on a six-sided die as the success and any other number as failure. Then the number of rolls before 5 occurs three times in a row can be defined as a negative binomial experiment.

The probability mass function of a negative binomial random variable <em>X</em> is:

P(X=k)={{k+r-1}\choose k}\cdot (1-p)^{k}\cdot p^{r};\ k=1,2,3,...

Here,

<em>k</em> = number of successes

<em>r</em> = number of failures

<em>p</em> = probability of success

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BaLLatris [955]

Answer:

y = -(5/2)x -2

Explanation:

The general formula for a straight line is y – mx + b.

The image below shows the graph of the line.

Step 1. <em>Calculate the slope</em>.

Slope = m = Δy/Δx = (y₂-y₁)/(x₂-x₁)

x₁ = 0; y₁ = -2

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m = [3-(-2)]/(-2-0)

m = (3+2)/(-2)

m = 5/(-2)

m = -5/2

Step 2. <em>Calculate the y-intercept </em>

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Step 3. <em>Write the equation </em>for the graph

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3 0
3 years ago
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GuDViN [60]

Answer:

(-2, 11) and (2, 3)

Step-by-step explanation:

<u>Given system of equations:</u>

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2) f(x) = -2x + 7 ⇒ y = -2x + 7

Solve Using the Substitution Method:

<u>Step 1:</u> Substitute the the first equation into the second.

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<u>Step 2:</u> Solve for x.

x² - 2x + 3 = -2x + 7 [ Add 2x to both sides. ]

x² - 2x + 2x + 3 = -2x + 2x + 7

⇒ x² + 3 = 7 [ Subtract 3 from both sides. ]

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<u>Step 3:</u> Solve for y.

<em>Substitute the found x-values into one of the given equations.</em>

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The solutions to the system of equations are: (-2, 11) and (2, 3).

Learn more about system of equations here:

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What’s equivalent (2x^5)^3
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Answer:

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Step-by-step explanation:

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