Calculators & Converters

    PDF of Triangular Distribution for a =4.5, b = 7.2, c = 5.5 & x = 12

    Triangular Distribution Calculator

    Triangular distribution example problem workout with steps & calculation summary for the probabilty of random variable x = 12 lies between two points a = 4.5 & b = 7.2 and mid-point c = 5.5, along with mean, median, mode and variance estimation in statistical experiments.

    Calculation Summary
    a 4.5
    b7.2
    c5.5
    x12
    PDF 0
    Mean µ5.7333
    Median 5.6851
    Mode 5.5
    Variance σ20.3106

    Work with steps for a = 4.5, b = 7.2, c = 5.5 & x = 12

    Question:
    Find the probability density function P(x) for random variable x = 12 which follows Triangular distribution having the lower limit a = 4.5, upper limit b = 7.2 and height c = 5.5
    workout :
    step 1 Address the formula input parameters & values
    a = 4.5
    b = 7.2
    c = 5.5
    x = 12

    step 2Find PDF value
    x > b value
    PDF = 0

    step 3 Find Mean using a, b & c values
    Mean = a + b + c/2
    = 4.5 + 7.2 + 5.5/2
    = 17.2/3
    Mean µ = 5.7333

    step 4 Find Median value using a, b & c values
    Median = b -(b - a)(b - c)/2
    = 7.2 - (7.2 - 4.5)(7.2 - 5.5)/2
    = 7.2 - (2.7)(1.7)/2
    = 7.2 - 4.59/2
    = 7.2 - √2.295
    = 7.2 - 1.5149
    Median = 5.6851

    step 5 Find Mode value
    Mode = c
    Mode = 5.5

    step 6 Find variance using a, b and c values
    Variance σ2 = a² + b² + c² - ab - ac - bc/18
    = (4.5)² + (7.2)² + (5.5)² - (4.5 x 7.2) - (4.5 x 5.5) - (7.2 x 5.5)/18
    = 20.25 + 51.84 + 30.25 - 32.4 - 24.75 - 39.6/18
    = 102.34 - 96.75/18
    = 5.59/18
    Variance σ² = 0.3106

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