Ideas and execution are not independent. For example, it is easier to execute an idea that you believe in rather than one you don't. (In a vacuum it may seem strange to think that someone would execute an idea that they don't believe in, but realize that this happens all the time, perhaps the majority of time). Another example, it is easier to execute an idea which actually has a market - the enthusiasm of customers is infectious and highly motivating. Final example, execution is better when the idea 'goes with the grain' of available technology (if it's a technology idea, of course).
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Ideas and execution are not independent. For example, it is easier to execute an idea that you believe in rather than one you don't. (In a vacuum it may seem strange to think that someone would execute an idea that they don't believe in, but realize that this happens all the time, perhaps the majority of time). Another example, it is easier to execute an idea which actually has a market - the enthusiasm of customers is infectious and highly motivating. Final example, execution is better when the idea 'goes with the grain' of available technology (if it's a technology idea, of course).