Let X Bin(7, 0.3). Find a. P(X = 1) b. P(X = 2) c. P(X < 1) d. P(X > 4) e. X f. 2

Chapter 4, Problem 1

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QUESTION:

Let \(X \sim \operatorname{Bin}(7,0.3)\). Find

a. \(P(X=1)\)

b.  \(P(X=2)\)

c.  \(P(X<1)\)

d.  \(P(X>1)\)

e.  \(\mu_{x}\)

f.  \(\sigma_{x}^{2}\)

Equation Transcription:

Text Transcription:

X \sim Bin(7, 0.3)

P(X=1)

P(X=2)

P(X<1)

P(X>1)

\mu_x

\sigma_x^2

Questions & Answers

QUESTION:

Let \(X \sim \operatorname{Bin}(7,0.3)\). Find

a. \(P(X=1)\)

b.  \(P(X=2)\)

c.  \(P(X<1)\)

d.  \(P(X>1)\)

e.  \(\mu_{x}\)

f.  \(\sigma_{x}^{2}\)

Equation Transcription:

Text Transcription:

X \sim Bin(7, 0.3)

P(X=1)

P(X=2)

P(X<1)

P(X>1)

\mu_x

\sigma_x^2

ANSWER:

Problem 1

Let . Find

(a)

(b)

(c)

(d)

(e)

(f)

                                                              Step by Step Solution

Step 1 of 5

Given that

To find

It is known that for a discrete random variable following binomial distribution with parameters and , its probability mass function is defined as

           (i)

Mean and variance of are defined by

             (ii)

   (iii)

For the given problem,

Then,

So, the value of  is 0.2471

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