1 Find the value of C to that the function probability density function defined as follow, also calculate the man and variance /4

Question

1 Find the value of C to that the function probability density function defined as follow, also calculate the man and variance /4

X -1 0 1
f(x) 3c 3c 6c

in progress 0
Khoii Minh 5 years 2021-08-04T10:02:33+00:00 1 Answers 12 views 0

Answers ( )

  1. RuslanHeatt
    0
    2021-08-04T10:03:52+00:00
    Reply

    Answer:

    c = \frac{1}{12}

    The mean of the distribution is 0.25.

    The variance of the distribution is of 0.6875.

    Step-by-step explanation:

    Probability density function:

    For it to be a probability function, the sum of the probabilities must be 1. The probabilities are 3c, 3c and 6c, so:

    3c + 3c + 6c = 1

    12c = 1

    c = \frac{1}{12}

    So the probability distribution is:

    P(X = -1) = 3c = 3\frac{1}{12} = \frac{1}{4} = 0.25

    P(X = 0) = 3c = 3\frac{1}{12} = \frac{1}{4} = 0.25

    P(X = 1) = 6c = 6\frac{1}{12} = \frac{1}{2} = 0.5

    Mean:

    Sum of each outcome multiplied by its probability. So

    E(X) = -1(0.25) + 0(0.25) + 1(0.5) = -0.25 + 0.5 = 0.25

    The mean of the distribution is 0.25.

    Variance:

    Sum of the difference squared between each value and the mean, multiplied by its probability. So

    V^2(X) = 0.25(-1-0.25)^2 + 0.25(0 - 0.25)^2 + 0.5(1 - 0.25)^2 = 0.6875

    The variance of the distribution is of 0.6875.

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )