Probability of X in [-0.25, 0.75] Explained

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In summary, the conversation discusses the meaning and calculation of the probability of a variable X falling within a given range, specifically [-0.25, 0.75]. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes or by finding the area under a probability distribution curve. The probability of X in this range can provide valuable information for making predictions and decisions. It cannot be greater than 1, and a wider range will result in a lower probability.
  • #1
ahamdiheme
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Assuming i have plotted my pdf and cdf functions which lie in the interval [-1, 1] what does P[[tex]\left|X-0.5|[/tex]<0.25] imply? The part i am not clear on is the [tex]\left|X-0.5|[/tex] part. Please clear me out on this
 
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  • #2
|X-0.5|<0.25 simply means 0.25<X<0.75.
 
  • #3
I was just posting an apology when this came in. I did not think b4 asking (basic absolute value stuff) thanks any way. I need a walk
 

1. What does the probability of X in [-0.25, 0.75] mean?

The probability of X in [-0.25, 0.75] refers to the likelihood of the variable X falling within the range of -0.25 and 0.75. This is typically expressed as a decimal or percentage.

2. How is the probability of X calculated?

The probability of X is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In the case of a continuous range like [-0.25, 0.75], the probability is determined by finding the area under the curve of the probability distribution function within that range.

3. What is the significance of the probability of X in [-0.25, 0.75]?

The probability of X in [-0.25, 0.75] can provide valuable information about the likelihood of a certain event or outcome occurring within that range. It can also be used to make predictions and inform decision-making processes.

4. Can the probability of X be greater than 1?

No, the probability of X cannot be greater than 1. This would indicate a probability of more than 100%, which is not possible. The probability of X can range from 0 to 1, with 0 indicating impossibility and 1 indicating certainty.

5. How does the range of [-0.25, 0.75] affect the probability of X?

The range of [-0.25, 0.75] directly affects the probability of X, as it determines the possible outcomes that are included in the calculation. A wider range will typically result in a lower probability, while a narrower range will result in a higher probability.

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