How do you find the mean of the random variable #x#?

X= 5,10,15,20,25
P(x) = 1/5, 1/5 , 1/5, 1/5, 1/5

What is the variance and standard deviation of the random variable #x#?
What is the standard deviation of the random variable #x#?

Answer 1

#"mean " E(X)=15#

#Var(X)=50#

#sd=7.07#

For a probability distribution

#color(red)(E(X)=sum_(all x)xP(X=x))---(1)#

in this case we have

#E(X)=5xx1/5+10xx1/5+15xx1/5+20xx1/5+25xx1/5#
#E(X)=1+2+3+4+5#
#E(X)=15#

the variance is calculated by

#color(blue)(Var(X)=E(X^2)-E^"(X))---(2)#
where #color(blue)(E(X^2)=sum_(allx)x^2P(X=x)--(3))#
#E(X^2)=5^2xx1/5+10^2xx1/5+15^2xx1/5+20^2xxx1/5+25^2xx1/5#
#E(X^")=1/5(25+100+225+400+625)#
#E(X^2)=275.#
#Var(X)=275-15^2=275-225=50#
#sd=sqrtVar(X)=sqrt50=7.07#
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Answer 2

To find the mean of a random variable ( x ), you calculate the sum of all possible values of ( x ) multiplied by their respective probabilities, then divide by the total number of possible values or trials. Mathematically, it's expressed as:

[ \text{Mean} (\mu) = \sum_{i=1}^{n} x_i \cdot P(x_i) ]

Where:

  • ( x_i ) represents each possible value of the random variable.
  • ( P(x_i) ) represents the probability associated with each value ( x_i ).
  • ( n ) is the total number of possible values or trials.

By summing up ( x_i \cdot P(x_i) ) for all possible values of ( x ), you obtain the mean of the random variable ( x ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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