Solve In R programmning language: Calculate the probability for each of the following events: (a) A standard normally distributed variable is less than -2.5. (b) A normally distributed variable with mean 35 and standard deviation 6 is larger than 42 but less than 45. (c) A normally distributed variable with mean 35 and standard deviation 6 is larger than 40 but less than 41. (d) X < 0.9 when X has the standard uniform distribution (min=0, max=1). (e) 1 < X < 3 in the exp distribution with rate λ = 2.

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Solve In R programmning language:

  1. Calculate the probability for each of the following events:

(a) A standard normally distributed variable is less than -2.5.

(b) A normally distributed variable with mean 35 and standard deviation 6 is larger than 42 but less than 45.

(c) A normally distributed variable with mean 35 and standard deviation 6 is larger than 40 but less than 41.

(d) X < 0.9 when X has the standard uniform distribution (min=0, max=1).

(e) 1 < X < 3 in the exp distribution with rate λ = 2.

2. Calculate the probability for each of the following events:
(a) A standard normally distributed variable is less than -2.5.
(b) A normally distributed variable with mean 35 and standard deviation 6 is larger than 42 but less than
45.
(c) A normally distributed variable with mean 35 and standard deviation 6 is larger than 40 but less than
41.
(d) X < 0.9 when X has the standard uniform distribution (min=0, max=1).
(e) 1<X<3 in the exp distribution with rate A = 2.
Transcribed Image Text:2. Calculate the probability for each of the following events: (a) A standard normally distributed variable is less than -2.5. (b) A normally distributed variable with mean 35 and standard deviation 6 is larger than 42 but less than 45. (c) A normally distributed variable with mean 35 and standard deviation 6 is larger than 40 but less than 41. (d) X < 0.9 when X has the standard uniform distribution (min=0, max=1). (e) 1<X<3 in the exp distribution with rate A = 2.
2. Calculate the probability for each of the following events:
(a) A standard normally distributed variable is less than -2.5.
(b) A normally distributed variable with mean 35 and standard deviation 6 is larger than 42 but less than
45.
(c) A normally distributed variable with mean 35 and standard deviation 6 is larger than 40 but less than
41.
(d) X < 0.9 when X has the standard uniform distribution (min=0, max=1).
(e) 1<X<3 in the exp distribution with rate A = 2.
Transcribed Image Text:2. Calculate the probability for each of the following events: (a) A standard normally distributed variable is less than -2.5. (b) A normally distributed variable with mean 35 and standard deviation 6 is larger than 42 but less than 45. (c) A normally distributed variable with mean 35 and standard deviation 6 is larger than 40 but less than 41. (d) X < 0.9 when X has the standard uniform distribution (min=0, max=1). (e) 1<X<3 in the exp distribution with rate A = 2.
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