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The likelihood function is not a probability distribution because its integral over the parameter space does not equal 1. It measures how well each parameter value explains the fixed data, rather than assigning probabilities to the parameter values themselves.

Conditions: The data are fixed.; The parameter $p$ is varied over its space $[0,1]$.

The likelihood function is not a probability distribution because its integral over the parameter space does not equal 1. It measures how well each parameter value explains the fixed data, rather than assigning probabilities to the parameter values themselves.

Conditions: The data are fixed.; The parameter $p$ is varied over its space $[0,1]$.

The probability distribution sums to 1 because it accounts for all possible data outcomes under a fixed model, satisfying the axioms of probability. The likelihood curve does not integrate to 1 because it measures relative support for different parameter values given fixed data, and is not constrained to be a probability distribution over the parameter space.

Conditions: Probability view: parameter fixed, data varies over the entire sample space.; Likelihood view: data fixed, parameter varies over its domain.

The probability distribution sums to 1 because it accounts for all possible data outcomes under a fixed model, satisfying the axioms of probability. The likelihood curve does not integrate to 1 because it measures relative support for different parameter values given fixed data, and is not constrained to be a probability distribution over the parameter space.

Conditions: Probability view: parameter fixed, data varies over the entire sample space.; Likelihood view: data fixed, parameter varies over its domain.

Among the tested parameter values, $p=0.7$ yields the highest likelihood for the observed data. The likelihood measures how well each candidate value of $p$ explains the fixed observation of 7 heads in 10 flips.

Conditions: The observed data are fixed at 7 heads in 10 flips.; The candidate values tested are $p=0.3, 0.5,$ and $0.7$.

Among the tested parameter values, $p=0.7$ yields the highest likelihood for the observed data. The likelihood measures how well each candidate value of $p$ explains the fixed observation of 7 heads in 10 flips.

Conditions: The observed data are fixed at 7 heads in 10 flips.; The candidate values tested are $p=0.3, 0.5,$ and $0.7$.