5.5.3 Suppose X and Y have a bivariate normal distribution with , , , , and . Determine the following. Round your answers to three decimal places (e. g. 98.765). (a) Enter your answer in accordance to the item a) of the question statement (b) Enter your answer in accordance to the item b) of the question statement (c) Enter your answer in accordance to the item c) of the question statement

The question is incomplete. The complete question is :

Suppose X and Y have a bivariate normal distribution with and ρ = 0.

Determine the following. Round your answers to three decimal places (e.g. 98.765).

(a).

(b).

(c). P(2.90 < X < 3.10, 9.60 < Y < 7.80) =

Solution :

We have

 and

a). The required probability is

  = P(-2.5 < Z < 2.5)  =  P(Z < 2.5) - P(Z < -2.5)

  = P(Z < 2.5) - [1-P(Z < 2.5)]

 = 2P(Z < 2.5) - 1

 = 2(0.99379) - 1

 = 0.98758

 ≈ 0.988

b). The required probability is

  = P(-1.25 < Z < 1.25)  =  P(Z < 1.25) - P(Z < -1.25)

  = P(Z < 1.25) - [1-P(Z < 1.25)]

 = 2P(Z < 1.25) - 1

 = 2(0.89435) - 1

 = 0.7887

 ≈ 0.789

c). Since, ρ = 0, so the X and Y are independent. Thus the required probability is :

P(2.90 < X < 3.10, 9.60 < Y < 7.80) = P(2.9 < X < 3.1) x P(7.6 < Y < 7.8)

     = (0.98758)(0.7887)

     = 0.77890

      ≈ 0.779

eveidence i thing that

step-by-step explanation:

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step-by-step explanation: