Using the geometric distribution with a success probability of 0.3, calculate P(X = k) on trial number 5

Using the geometric distribution with a success probability of 0.3, calculate the probability of exactly 1 success on trial number 5

Expected Frequency (skip if you are calculating probability):

Expected frequency = n x p
Expected frequency = 5 x 0.3
Expected frequency = 1.5

Determine our formula:
P(x = n) = p * (1 - p)^{(n - 1)}

Plug in our values:
P(x = 5) = 0.3 * (1 - 0.3)^{(5 - 1)}
P(x = 5) = 0.3 * 0.7⁴
P(x = 5) = 0.3 * 0.2401

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Now calculate the Mean (μ), Variance (σ²), and Standard Deviation (σ)

Calculate the mean μ:

μ  =	1
	p

μ  =	1
	0.3

μ = 3

Calculate the variance σ²:

σ2  =	1 - p
	p2

σ2  =	1 - 0.3
	0.32

σ2  =	0.7
	0.09

σ² = 7.7778

Calculate the standard deviation σ:
  σ  =  √σ²
  σ  =  √7.7778
σ = 2.7889

Calculate skewness:

Skewness  =	2 - p
	√1 - p

Skewness  =	2 - 0.3
	√1 - 0.3

Skewness  =	1.7
	√0.7

Skewness  =	1.7
	0.83666002653408

Skewness = 2.0318886358685

Calculate Kurtosis:

Kurtosis = 6 + p²/(1 - p)
Kurtosis = 6 + 0.3²/(1 - 0.3)
Kurtosis = 6 + 0.09/0.7
Kurtosis = 6 + 0.12857142857143
Kurtosis = 6.1285714285714