The P(X<0.2) with standard beta distribution parameters α = 5 and β = 2 is 0.0016.
How to calculated the probability density function in standard beta distribution?
Beta distribution is one of the continuous probability distributions set at interval (0, 1) intervals with two positive parameters α and β.
Probability density function can be calculated by this formula
[tex]\frac{x^{\alpha -1}(1-x)^{\beta -1}}{B(\alpha ,\beta) }[/tex]
B(α,β) is beta function = Γ(α)Γ(β)/Γ(α+β)
Γ(α) is gamma function of alpha
Γ(β) is gamma function of beta
P(X<0.2) = [tex]\frac{0.2^{5-1}(1-0.2)^{2-1}}{B(5,2) }[/tex]
= 0.0016
Excel formula for beta distribution is
=BETA.DIST(x;α;β;TRUE)
Thus, the P(X<0.2) with standard beta distribution parameters α = 5 and β = 2 is 0.0016.
Learn more about beta distribution here:
brainly.com/question/14468758
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