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algol13
2 years ago
15

Edg vector operations, any help appreciated!

Mathematics
1 answer:
viktelen [127]2 years ago
8 0

\quad \huge \quad \quad \boxed{ \tt \:Answer }

\qquad \tt \rightarrow \: Add \:\: -6 \hat i - 6\hat j \:\:with \:\; Vector \:\; c

____________________________________

\large \tt Solution  \: :

Vector d can be represented as :

\qquad \tt \rightarrow \:  - 2 \hat i - 2 \hat j

Vector c can be represented as :

\qquad \tt \rightarrow \:  4 \hat i + 4\hat j

we have to create vector d from vector c

So, let's assume a vector x, such that sum of vector x and vector c equals to vector d

\qquad \tt \rightarrow \: x + ( 4 \hat i + 4 \hat j) =  - 2 \hat i  - 2 \hat j

\qquad \tt \rightarrow \: x  = -  ( 4 \hat i + 4 \hat j)   - 2 \hat i  - 2 \hat j

\qquad \tt \rightarrow \: x  = (-   4 \hat i  - 2 \hat  i)  + (  - 4 \hat j  - 2 \hat j)

\qquad \tt \rightarrow \: x  = - 6 \hat  i    -6 \hat j

Henceforth, in order to get vector d, we need to add (-6i - 6j) in vector c

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

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For <em>X</em> = 1 the probability is:

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For <em>X</em> = 2 the probability is:

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Similarly the remaining probabilities will be computed.

The probability distribution table is shown below.

The histogram is also shown below.

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The expected value of a Binomial distribution is:

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E(X)=np=12\times0.35=4.2

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The standard deviation of a Binomial distribution is:

SD(X)=np(1-p)

The standard deviation of vehicles out of 12 that will tailgate is:

SD(X)=np(1-p)=12\times0.35\times(1-0.35)=2.73\\

Thus, the standard deviation of vehicles out of 12 that will tailgate is 2.73.

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