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The probability density of a random variable X is given in the figure below.

From this density, the probability that X is between 0.68 and 1.44 is:

Find the probability that X is between 0.68 and 1.44.

The probability density of a random variable X is given in the figure below. From this density, the probability that X is between 0.68 and 1.44 is: Find the pro class=

Answer :

MathPhys

Answer:

0.38

Step-by-step explanation:

The area under the probability density curve is equal to 1.

The width of the rectangle is 2, so the height of the rectangle must be ½.

The probability that X is between 0.68 and 1.44 is therefore:

P = ½ (1.44 − 0.68)

P = 0.38

Using the uniform distribution, it is found that there is a 0.38 = 38% probability that X is between 0.68 and 1.44.

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Uniform probability distribution:

  • Has two bounds, a and b.  
  • The probability of finding a value between c and d is:

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

In this problem:

  • The bounds are 0 and 2, thus [tex]a = 0, b = 2[/tex].

The probability that X is between 0.68 and 1.44 is:

[tex]P(0.68 \leq X \leq 1.44) = \frac{1.44 - 0.68}{2 - 0} = 0.38[/tex]

0.38 = 38% probability that X is between 0.68 and 1.44.

A similar problem is given at https://brainly.com/question/13547683

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