# A random walk results in the random walker being in a position 7 4 units away from

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## Question:

A random walk results in the random walker being in a position $74$ units away from the origin after taking $44$ steps.

a$)$ Is this result possible $=$

b$)$ What is the probability of this result happening

Use scientific notation with $2$ decimal places in the format $0\mathrm{.}00012345\text{}\backslash "">=\text{}\backslash "">$E$-4$ WITHOUT multiplying by $100\%$

If not possible, write NA

$=$

A random walk results in the random walker being in a position $29$ units away from the origin after taking $81$ steps.

a$)$ Is this result possible $=$

b$)$ What is the probability of this result happening

Use scientific notation with $2$ decimal places in the format $0\mathrm{.}00012345\text{}\backslash "">=\text{}\backslash "">$E$-4$ WITHOUT multiplying by $100\%$

If not possible, write NA

$=$Calculate the probability of a dust particle floating on air to be at a position $39$ units given $218$ seconds to move.

Use scientific notation with $2$ decimal places in the format $0\mathrm{.}00012345\text{}\backslash "">=\text{}\backslash "">$E$-4$ WITHOUT multiplying by $100\%.$

Note that for stochastic processes, even values of a which are not divisible by $2$ can still have a probability of happening.

Also, there is no if a process is not possible, you just indicate it\'s probability of happening as zero.

Calculate the probability of a dust particle floating on air to be at a position $62$ units given $127$ seconds to move.

Use scientific notation with $2$ decimal places in the format $0\mathrm{.}00012345\text{}\backslash "">=\text{}\backslash "">$E$-4$ WITHOUT multiplying by $100\%.$

Note that for stochastic processes, even values of a which are not divisible by $2$ can still have a probability of happening.

Also, there is no if a process is not possible, you just indicate it\'s probability of happening as zero.Calculate the probability of a dust particle floating on air to be at a position $89$ units given $109$ seconds to move.

Use scientific notation with $2$ decimal places in the format $0\mathrm{.}00012345\text{}\backslash "">=\text{}\backslash "">$E$-4$ WITHOUT multiplying by $100\%.$

Note that for stochastic processes, even values of a which are not divisible by $2$ can still have a probability of happening.

Also, there is no if a process is not possible, you just indicate it\'s probability of happening as zero.

Upon unloading a bag of cement on a riverbank, some cement dust falls into the fresh water.

Given the following conditions:

Diameter of cement dust $=\text{}\backslash "">3$ microns $(1$ micron $=\text{}\backslash "">10^-6$ m$)$

Temperature $=\text{}\backslash "">22$ degrees Celsius

Viscosity of river water $=\text{}\backslash "">0\mathrm{.}9544$ mPa$*$s

Moles of cement dust particles $=\text{}\backslash "">8$ moles

a$)$ Calculate the Stokes$-$Einstein Diffusion Coefficient for the system

Use scientific notation with $2$ decimal places in the format $0\mathrm{.}00012345\text{}\backslash "">=\text{}\backslash "">$E$-4$

$=$

square millimeters$/$second

b$)$ Calculate p$(3\mathrm{.}7$ mm$,\text{}\backslash "">36400$ s$)$

Use scientific notation with $2$ decimal places in the format $0\mathrm{.}00012345\text{}\backslash "">=\text{}\backslash "">$E$-4$ WITHOUT multiplying by $100\%$

$=$

THESE ARE ALL THE QUESTIONS ABOUT RANDOM WALKS AND DIFFUSIONS. HELP ME ANSWER EACH.